The Once and Future Cosmos - My search · 2014-05-08 · CHAIRMAN EMERITUS: John J. Hanley CHAIRMAN: Rolf Grisebach PRESIDENT AND CHIEF EXECUTIVE OFFICER: Gretchen G. Teichgraeber

•Echoes from the Big Bang

•Does Space Have Borders?

•Parallel Universes

•Energy in Empty Space?

•The Fate of All Life

•Dark Energy and Dark Matter

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Making Sense of Modern Cosmology by P. James E. PeeblesConfused about all the theories? Good.

The First Starsin the Universeby Richard B. Larson and Volker BrommExceptionally massive and bright, the earliest stars changed the course of cosmic history.

The Life Cycle of Galaxiesby Guinevere Kauffmann and Frank van den BoschAstronomers are on the verge of explaining the bewildering variety of galaxies.

Surveying Spacetime with Supernovaeby Craig J. Hogan, Robert P. Kirshner and Nicholas B. SuntzeffExploding stars seen across immense distances show thatthe cosmic expansion may be accelerating—a sign that anexotic form of energy could be driving the universe apart.

Cosmological Antigravityby Lawrence M. KraussThe long-derided cosmological constant—a contrivance of Albert Einstein’s—may explain changesin the expansion rate of the universe.

The Quintessential Universeby Jeremiah P. Ostriker and Paul J. SteinhardtThe universe has recently been commandeered by an invisible energy field, which is causing its expansion to accelerate outward.

The Fate of Lifein the Universeby Lawrence M. Krauss and Glenn D. StarkmanBillions of years ago the universe was too hot for life toexist. Countless aeons from now, it will become so coldand empty that life, no matter how ingenious, will perish.

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Cone Nebula, captured in April 2002 by the Hubble Space Telescope

cosmosthe once and futurethe once and future

INTRODUCTION

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SCIENTIFIC AMERICAN Volume 12 Number 2

contents

SCIENTIFIC AMERICAN Volume 12 Number 2cosmos

EXPANSION

EVOLUTION

COPYRIGHT 2002 SCIENTIFIC AMERICAN, INC.

A Cosmic Cartographerby Charles L. Bennett, Gary F. Hinshaw and Lyman PageThe Microwave Anisotropy Probe will provide a much sharper picture of the early universe.

Echoes from the Big Bangby Robert R. Caldwell and Marc KamionkowskiScientists may soon glimpse the universe’s beginningsby studying subtle fluctuations in the cosmic microwave background.

Exploring Our Universe and Othersby Martin ReesIn this century cosmologists will unravel the mystery of our universe’s birth—and perhaps prove theexistence of other universes as well.

Ripples in Spacetimeby W. Wayt GibbsLIGO, a controversial observatory for detecting gravitational waves, is coming online after eight yearsand $365 million.

Plan B for the Cosmosby João MagueijoIf the new cosmology fails, what’s the backup plan?

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S c i e n t i f i c A m e r i c a n S p e c i a l ( I S S N 10 4 8 - 0 9 4 3 ) , V o l u m e 1 2 , N u m b e r 2 , 2 0 0 2 , p u b l i s h e d b yS c i e n t i f i c A m e r i c a n , I n c . , 415 M a d i s o n A v e n u e , N e w Y o r k , N Y 10 017- 1 1 1 1 . C o p y r i g h t © 2 0 0 2 b y S c i e n t i f i c A m e r i c a n , I n c . A l l r i g h t s r e s e r v e d . N o p a r t o f t h i s i s s u e m a y b e r e p r o d u c e d b y a n ym e c h a n i c a l , p h o t o g r a p h i c o r e l e c t r o n i c p r o c e s s , o r i n t h e f o r m o f a p h o n o g r a p h i c r e c o r d i n g , n o rm a y i t b e s t o r e d i n a r e t r i e v a l s y s t e m , t r a n s m i t t e d o r o t h e r w i s e c o p i e d f o r p u b l i c o r p r i v a t e u s ewithout written per m ission of the publisher. Canadian BN No. 127387652RT; QST No. Q1015332537.To purchase addit ional quantit ies: 1 to 9 copies: U.S. $5.95 each plus $2.00 per copy for postageand handling (outside U.S. $5.00 P&H). Send payment to Scientific American, D e p t . C O S M , 415 M a d i s o n A v e n u e , New York, NY 10017-1111. Inquir ies: Fax 212-355-0408 or telephone 212-451-8890. Printed in U.S.A.

Cover illustration by Edwin Faughn; NASA/Associated Press(opposite page); Bryan Christie Design (left and above)

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58 Is Space Finite?by Jean-Pierre Luminet, Glenn D. Starkman and Jeffrey R. WeeksConventional wisdom says the universe is infinite. But it could be finite, merely giving the illusion of infinity. Upcoming measurements may finally resolve the issue.

The Universe’s Unseen Dimensionsby Nima Arkani-Hamed, Savas Dimopoulos and Georgi DvaliThe visible universe could lie on a membrane floating in a higher-dimensional space. The extra dimensions would help unify the forces of nature and could hold parallel universes.

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Spheres of gravitational influence, page 66

“Infinity box” creates the effect with mirrors, page 58

STRUCTUREDESTINY

w w w . s c i a m . c o m T H E O N C E A N D F U T U R E C O S M O S 1COPYRIGHT 2002 SCIENTIFIC AMERICAN, INC.

T his is an exciting time for cosmologists: findings are pouring in, ideasare bubbling up, and research to test those ideas is simmering away. Butit is also a confusing time. All the ideas under discussion cannot possi-bly be right; they are not even consistent with one another. How is oneto judge the progress? Here is how I go about it. µµµµµµµµµµµµµ

For all the talk of overturned theories, cosmologists have firmly es-tablished the foundations of our field. Over the past 70 years we have gathered abun-dant evidence that our universe is expanding and cooling. First, the light from dis-tant galaxies is shifted toward the red, as it should be if space is expanding and gal-axies are pulled away from one another. Second, a sea of thermal radiation fillsspace, as it should if space used to be denser and hotter. Third, the universe containslarge amounts of deuterium and helium, as it should if temperatures were once muchhigher. Fourth, distant galaxies, seen as they were in the past because of light’s trav-el time, look distinctly younger, as they should if they are closer to the time when nogalaxies existed. Finally, the curvature of spacetime seems to be related to the ma-terial content of the universe, as it should be if the universe is expanding accordingto the predictions of Einstein’s gravity theory, the general theory of relativity.

That the universe is expanding and cooling is the essence of the big bang theo-ry. You will notice I have said nothing about an “explosion”—the big bang theorydescribes how our universe is evolving, not how it began.

I compare the process of establishing such compelling results, in cosmology orany other science, to the assembly of a framework. We seek to reinforce each pieceof evidence by adding cross bracing from diverse measurements. Our frameworkfor the expansion of the universe is braced tightly enough to be solid. The big bangtheory is no longer seriously questioned; it fits together too well. Even the most rad-ical alternative—the latest incarnation of the steady state theory—does not disputethat the universe is expanding and cooling. You still hear differences of opinion incosmology, to be sure, but they concern additions to the solid part.

For example, we do not know what the universe was doing before it was ex-panding. A leading theory, inflation, is an attractive addition to the framework, butit lacks cross bracing. That is precisely what cosmologists are now seeking. If mea-

P. JAMES E. PEEBLES is one of the world’s most distinguished cosmologists, a key playerin the early analysis of the cosmic microwave background radiation and the bulk compo-sition of the universe. He has received some of the highest awards in astronomy, includ-ing the 1982 Heineman Prize, the 1993 Henry Norris Russell Lectureship of the Ameri-can Astronomical Society and the 1995 Bruce Medal of the Astronomical Society of the Pa-cific. He is emeritus professor at Princeton University.TH

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Confused by all those theories? GoodThe Once and Future Cosmos is published by the staff ofScientific American, with project management by:

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making senseof moderncosmology

BY P. JAMES E. PEEBLES

2 S C I E N T I F I C A M E R I C A N U p d a t e d f r o m t h e J a n u a r y 2 0 0 1 i s s u e

INTR

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surements in progress agree with the unique signatures of in-flation, then we will count them as a persuasive argument forthis theory. But until that time, I would not settle any bets onwhether inflation really happened. I am not criticizing the the-ory; I simply mean that this is brave, pioneering work still tobe tested.

More solid is the evidence that most of the mass of the uni-verse consists of dark matter clumped around the outer parts ofgalaxies. We also have a reasonable case for Einstein’s infamouscosmological constant or something similar; it would be theagent of the acceleration that the universe now seems to be un-dergoing. A decade ago cosmologists generally welcomed darkmatter as an elegant way to account for the motions of stars andgas within galaxies. Most researchers, however, had a real dis-taste for the cosmological constant. Now the majority accept it,or its allied concept, quintessence. Particle physicists have cometo welcome the challenge that the cosmological constant posesfor quantum theory. This shift in opinion is not a reflection ofsome inherent weakness; rather it shows the subject in a healthystate of chaos around a slowly growing fixed framework. Westudents of nature adjust our concepts as the lessons continue.

The lessons, in this case, include the signs that cosmic ex-pansion is accelerating: the brightness of supernovae near andfar; the ages of the oldest stars; the bending of light around dis-tant masses; and the fluctuations of the temperature of the ther-mal radiation across the sky. The evidence is impressive, but Iam still skeptical about details of the case for the cosmologicalconstant, including possible contradictions with the evolutionof galaxies and their spatial distribution. The theory of the ac-celerating universe is a work in progress. I admire the architec-ture, but I would not want to move in just yet.

How might one judge reports in the media on the progressof cosmology? I feel uneasy about articles based on an interview

with just one person. Research is a complex and messy business.Even the most experienced scientist finds it hard to keep every-thing in perspective. How do I know that this individual hasmanaged it well? An entire community of scientists can head offin the wrong direction, too, but it happens less often. That iswhy I feel better when I can see that the journalist has consult-ed a cross section of the community and has found agreementthat a certain result is worth considering. The result becomesmore interesting when others reproduce it. It starts to becomeconvincing when independent lines of evidence point to thesame conclusion. To my mind, the best media reports on sciencedescribe not only the latest discoveries and ideas but also the es-sential, if sometimes tedious, process of testing and installing thecross bracing.

Over time, inflation, quintessence and other concepts nowunder debate either will be solidly integrated into the centralframework or will be abandoned and replaced by somethingbetter. In a sense, we are working ourselves out of a job. Butthe universe is a complicated place, to put it mildly, and it is sil-ly to think we will run out of productive lines of research any-time soon. Confusion is a sign that we are doing somethingright: it is the fertile commotion of a construction site.

w w w . s c i a m . c o m T H E O N C E A N D F U T U R E C O S M O S 3

The Evolution of the Universe. P. James E. Peebles, David N. Schramm,Edwin L. Turner and Richard G. Kron in Scientific American, Vol. 271, No. 4,pages 52–57; October 1994.

The Inflationary Universe: The Quest for a New Theory of CosmicOrigins. Alan H. Guth. Perseus Press, 1997.

Before the Beginning: Our Universe and Others. Martin Rees. Perseus Press, 1998.

The Accelerating Universe: Infinite Expansion, the CosmologicalConstant, and the Beauty of the Cosmos. Mario Livio and Allan Sandage.John Wiley & Sons, 2000.

M O R E T O E X P L O R E

REPORT CARD FOR MAJOR THEORIES

Concept Grade CommentsThe universe evolved from a hotter, denser state A+ Compelling evidence drawn from many

corners of astronomy and physics

The universe expands as the general theory of relativity predicts A–

Passes the tests so far, but few of the testshave been tight

Dark matter made of exotic particles dominates galaxies B+

Most of the mass of the universe is smoothlydistributed; it acts like Einstein’s cosmologicalconstant, causing the expansion to accelerate

Encouraging fit from recent measurements, but more must be done to improve the evidenceand resolve the theoretical conundrums

The universe grew out of inflationInc

Elegant, but lacks direct evidence and requireshuge extrapolation of the laws of physics

Many lines of indirect evidence, but theparticles have yet to be found and alternativetheories have yet to be ruled out

B–


4 S C I E N T I F I C A M E R I C A N U p d a t e d f r o m t h e D e c e m b e r 2 0 0 1 i s s u e

UNIVERSESTARSIN THE

FIRST

BY RICHARD B. LARSONAND VOLKER BROMM

ILLUSTRATIONS BY DON DIXON

Exceptionally massive and bright, the earliest stars changed the course of cosmic history

WE LIVE IN A UNIVERSE that is full of bright objects. On a clear night one can see thousands ofstars with the naked eye. These stars occupy mere-ly a small nearby part of the Milky Way galaxy; tele-scopes reveal a much vaster realm that shineswith the light from billions of galaxies. According toour current understanding of cosmology, howev-er, the universe was featureless and dark for a longstretch of its early history. The first stars did notappear until perhaps 100 million years after thebig bang, and nearly a billion years passed beforegalaxies proliferated across the cosmos. Astron-omers have long wondered: How did this dramat-ic transition from darkness to light come about?

THEEVOL

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EARLIEST COSMIC STRUCTURE most likely took the form of a network of filaments. The first protogalaxies, small-scale systems about 30 to 100 light-yearsacross, coalesced at the nodes of this network. Inside the protogalaxies, the denser regions of gas collapsed to form the first stars (inset).

EARLIEST COSMIC STRUCTURE most likely took the form of a network of filaments. The first protogalaxies, small-scale systems about 30 to 100 light-yearsacross, coalesced at the nodes of this network. Inside the protogalaxies, the denser regions of gas collapsed to form the first stars (inset).


After decades of study, researchershave recently made great strides towardanswering this question. Using sophisti-cated computer simulation techniques,cosmologists have devised models thatshow how the density fluctuations leftover from the big bang could haveevolved into the first stars. In addition,observations of distant quasars have al-lowed scientists to probe back in timeand catch a glimpse of the final days ofthe “cosmic dark ages.”

The new models indicate that the firststars were most likely quite massive andluminous and that their formation wasan epochal event that fundamentallychanged the universe and its subsequentevolution. These stars altered the dy-namics of the cosmos by heating and ion-izing the surrounding gases. The earlieststars also produced and dispersed the firstheavy elements, paving the way for theeventual formation of solar systems likeour own. And the collapse of some of thefirst stars may have seeded the growth ofsupermassive black holes that formed inthe hearts of galaxies and became thespectacular power sources of quasars. Inshort, the earliest stars made possible theemergence of the universe that we see to-day—everything from galaxies and qua-sars to planets and people.

The Dark AgesTHE STUDY of the early universe is ham-pered by a lack of direct observations. As-tronomers have been able to examinemuch of the universe’s history by trainingtheir telescopes on distant galaxies andquasars that emitted their light billions

of years ago. The age of each object canbe determined by the redshift of its light,which shows how much the universe hasexpanded since the light was produced.The oldest galaxies and quasars that havebeen observed so far date from about abillion years after the big bang (assuminga present age for the universe of about 14billion years). Researchers will need bet-ter telescopes to see more distant objectsdating from still earlier times.

Cosmologists, however, can make de-ductions about the early universe basedon the cosmic microwave background ra-diation, which was emitted about 400,000years after the big bang. The uniformityof this radiation indicates that matter wasdistributed very smoothly at that time.Because there were no large luminous ob-jects to disturb the primordial soup, itmust have remained smooth and feature-less for millions of years afterward. As thecosmos expanded, the background radi-ation redshifted to longer wavelengthsand the universe grew increasingly coldand dark. Astronomers have no observa-tions of this dark era. But by a billionyears after the big bang, some brightgalaxies and quasars had already ap-peared, so the first stars must have formedsometime before. When did these first lu-minous objects arise, and how might theyhave formed?

Many astrophysicists, including Mar-tin Rees of the University of Cambridgeand Abraham Loeb of Harvard Universi-ty, have made important contributionstoward solving these problems. The re-cent studies begin with the standard cos-mological models that describe the evo-

lution of the universe following the bigbang. Although the early universe wasremarkably smooth, the background ra-diation shows evidence of small-scaledensity fluctuations—clumps in the pri-mordial soup. The cosmological modelspredict that these clumps would gradual-ly evolve into gravitationally bound struc-tures. Smaller systems would form firstand then merge into larger agglomera-tions. The denser regions would take theform of a network of filaments, and thefirst star-forming systems—small proto-galaxies—would coalesce at the nodes ofthis network. In a similar way, the proto-galaxies would then merge to form galax-ies, and the galaxies would congregateinto galaxy clusters. The process is ongo-ing: although galaxy formation is nowmostly complete, galaxies are still assem-bling into clusters, which are in turn ag-gregating into a vast filamentary networkthat stretches across the universe.

According to the cosmological mod-els, the first small systems capable offorming stars should have appeared be-tween 100 million and 250 million yearsafter the big bang. These protogalaxieswould have been 100,000 to one milliontimes more massive than the sun andwould have measured about 30 to 100light-years across. These properties aresimilar to those of the molecular gasclouds in which stars are currently form-ing in the Milky Way, but the first pro-togalaxies would have differed in somefundamental ways. For one, they wouldhave consisted mostly of dark matter, theputative elementary particles that are be-lieved to make up about 90 percent ofthe universe’s mass. In present-day largegalaxies, dark matter is segregated fromordinary matter: over time, ordinarymatter concentrates in the galaxy’s innerregion, whereas the dark matter remainsscattered throughout an enormous out-er halo. But in the protogalaxies, the or-dinary matter would still have beenmixed with the dark matter.

The second important difference isthat the protogalaxies would have con-tained no significant amounts of any el-ements besides hydrogen and helium.The big bang produced hydrogen andhelium, but most of the heavier elements

6 S C I E N T I F I C A M E R I C A N T H E O N C E A N D F U T U R E C O S M O S

Computer simulations show that the first stars should have appeared between100 million and 250 million years after the big bang. They formed in small protogalaxies that evolved from density fluctuations in the early universe.

Because the protogalaxies contained virtually no elements besides hydrogenand helium, the physics of star formation favored the creation of bodies thatwere many times more massive and luminous than the sun.

Radiation from the earliest stars ionized the surrounding hydrogen gas. Somestars exploded as supernovae, dispersing heavy elements throughout theuniverse. The most massive stars collapsed into black holes. As protogalaxiesmerged to form galaxies, the black holes possibly became concentrated in thegalactic centers.

Overview/The First Stars


are created only by the thermonuclearfusion reactions in stars, so they wouldnot have been present before the firststars had formed. Astronomers use theterm “metals” for all these heavier ele-ments. The young metal-rich stars in theMilky Way are called Population I stars,and the old metal-poor stars are calledPopulation II stars; following this termi-nology, the stars with no metals at all—the very first generation—are sometimescalled Population III stars.

In the absence of metals, the physics ofthe first star-forming systems would havebeen much simpler than that of present-day molecular gas clouds. Furthermore,the cosmological models can provide, inprinciple, a complete description of theinitial conditions that preceded the firstgeneration of stars. In contrast, the starsthat arise from molecular gas clouds areborn in complex environments that havebeen altered by the effects of previous starformation. Therefore, scientists may findit easier to model the formation of thefirst stars than to model how stars format present. In any case, the problem is anappealing one for theoretical study, andseveral research groups have used com-puter simulations to portray the forma-tion of the earliest stars.

A group consisting of Tom Abel, GregBryan and Michael L. Norman (now atPennsylvania State University, the Mass-achusetts Institute of Technology and theUniversity of California at San Diego, re-spectively) has made the most realisticsimulations. In collaboration with PaoloCoppi of Yale University, we have donesimulations based on simpler assumptionsbut intended to explore a wider range ofpossibilities. Toru Tsuribe (now at OsakaUniversity in Japan) has made similar cal-culations using more powerful comput-ers. Fumitaka Nakamura and MasayukiUmemura (now at Niigata and Tsukubauniversities in Japan, respectively) haveworked with a more idealized simulation,but it has still yielded instructive results.Although these studies differ in variousdetails, they have all produced similar de-scriptions of how the earliest stars mighthave been born.

Let There Be Light!THE SIMULATIONS show that the pri-mordial gas clouds would typically format the nodes of a small-scale filamentarynetwork and then begin to contract be-cause of their gravity. Compressionwould heat the gas to temperatures above1,000 kelvins. Some hydrogen atoms

would pair up in the dense, hot gas, cre-ating trace amounts of molecular hydro-gen. The hydrogen molecules would thenstart to cool the densest parts of the gasby emitting infrared radiation after theycollided with hydrogen atoms. The tem-perature in the densest parts would dropto about 200 to 300 kelvins, reducing thegas pressure in these regions and hence al-lowing them to contract into gravitation-ally bound clumps.

This cooling plays an essential role inallowing the ordinary matter in the pri-mordial system to separate from the darkmatter. The cooling hydrogen settles intoa flattened rotating configuration that isclumpy and filamentary and possiblyshaped like a disk. But because the darkmatter particles would not emit radiationor lose energy, they would remain scat-tered in the primordial cloud. Thus, thestar-forming system would come to re-semble a miniature galaxy, with a disk ofordinary matter and a halo of dark mat-ter. Inside the disk, the densest clumps ofgas would continue to contract, andeventually some of them would undergoa runaway collapse and become stars.

The first star-forming clumps weremuch warmer than the molecular gasclouds in which most stars currently


After the emission of the cosmic microwave background radiation (about 400,000 years after thebig bang), the universe grew increasingly cold and dark. But cosmic structure graduallyevolved from the density fluctuations left over from the big bang.

1 MILLION YEARS100 MILLION YEARS

1 BILLION YEARS12 TO 14 BILLION YEARS

Bigbang

Emission of cosmic background

radiation Dark ages

First stars

Protogalaxymergers

Modern galaxies

First supernovaeand black holes. . . TO THE RENAISSANCE

The appearance of the first stars and protogalaxies(perhaps as early as 100 million years after the big bang) set off a chain of events that transformed the universe.

FROM THE DARK AGES . . .

COSMIC TIME LINE



PRIMEVAL TURMOILThe process that led to the creation of the first stars was verydifferent from present-day star formation. But the violent deathsof some of these stars paved the way for the emergence of theuniverse that we see today.

The cooling of the hydrogen allowedthe ordinary matter to contract,

whereas the dark matter remaineddispersed. The hydrogen settled into a diskat the center of the protogalaxy.

THE BIRTH AND DEATH OF THE FIRST STARS

2 The denser regions of gas contractedinto star-forming clumps, each

hundreds of times as massive as the sun.Some of the clumps of gas collapsed toform very massive, luminous stars.

3 Ultraviolet radiation from the starsionized the surrounding neutral

hydrogen gas. As more and more starsformed, the bubbles of ionized gas mergedand the intergalactic gas became ionized.

4

The first star-forming systems—smallprotogalaxies—consisted mostly of the

elementary particles known as dark matter(shown in red). Ordinary matter—mainlyhydrogen gas (blue)—was initially mixed withthe dark matter.

1

Gravitational attraction pulled theprotogalaxies toward one another.

The collisions most likely triggered starformation, just as galactic mergers do now.

6 Black holes possibly merged to form asupermassive hole at the protogalaxy’s

center. Gas swirling into this hole mighthave generated quasarlike radiation.

7A few million years later, at the end oftheir brief lives, some of the first stars

exploded as supernovae. The most massivestars collapsed into black holes.

5

Black hole

Supernova

Ultravioletradiation


form. Dust grains and molecules con-taining heavy elements cool the present-day clouds much more efficiently to tem-peratures of only about 10 kelvins. Theminimum mass that a clump of gas musthave to collapse under its gravity is calledthe Jeans mass, which is proportional tothe square of the gas temperature and in-versely proportional to the square root ofthe gas pressure. The first star-formingsystems would have had pressures simi-lar to those of present-day molecularclouds. But because the temperatures ofthe first collapsing gas clumps were al-most 30 times higher than those of mo-

lecular clouds, their Jeans mass wouldhave been almost 1,000 times larger.

In molecular clouds in the nearbypart of the Milky Way, the Jeans mass isroughly equal to the mass of the sun, andthe masses of the prestellar clumps ob-served in these clouds are about the same.If we scale up by a factor of almost 1,000,we can estimate that the masses of thefirst star-forming clumps would havebeen about 500 to 1,000 solar masses. Inagreement with this prediction, all thecomputer simulations mentioned aboveshowed the formation of clumps withmasses of several hundred solar massesor more.

Our group’s calculations suggest thatthe predicted masses of the first star-form-ing clumps are not very sensitive to the as-sumed cosmological conditions (for ex-ample, the exact nature of the initial den-sity fluctuations). In fact, the predictedmasses depend primarily on the physics ofthe hydrogen molecule and only secon-darily on the cosmological model or sim-ulation technique. One reason is that mo-lecular hydrogen cannot cool the gas be-low 200 kelvins, making this a lower limitto the temperature of the first star-formingclumps. Another is that the cooling frommolecular hydrogen becomes inefficientat the higher densities encountered whenthe clumps begin to collapse. At these den-

sities the hydrogen molecules collide withother atoms before they have time to emitan infrared photon; this raises the gas tem-perature and slows down the contractionuntil the clumps have built up to at leasta few hundred solar masses.

What was the fate of the first collaps-ing clumps? Did they form stars with sim-ilarly large masses, or did they fragmentinto many smaller parts and form manysmaller stars? The research groups havepushed their calculations to the point atwhich the clumps are well on their way toforming stars, and none of the simula-tions has yet revealed any tendency for

the clumps to fragment. This agrees withour understanding of present-day starformation; observations and simulationsshow that the fragmentation of star-forming clumps is typically limited to theformation of binary systems (two starsorbiting around each other). Fragmenta-tion seems even less likely to occur in theprimordial clumps, because the ineffi-ciency of molecular hydrogen coolingwould keep the Jeans mass high. The sim-ulations, however, have not yet deter-mined the final outcome of collapse withcertainty, and the formation of binarysystems cannot be ruled out.

Different groups have arrived at some-what different estimates of just how mas-sive the first stars might have been. Abel,Bryan and Norman have argued that thestars probably had masses no greater than300 solar masses. Our own work suggeststhat masses as high as 1,000 solar massesmight have been possible. Both predic-

tions might be valid in different circum-stances: the very first stars to form mighthave had masses no larger than 300 solarmasses, whereas stars that formed a littlelater from the collapse of larger proto-galaxies might have reached the higher es-timate. Quantitative predictions are diffi-cult because of feedback effects; as a mas-sive star forms, it produces intenseradiation and matter outflows that mayblow away some of the gas in the collaps-ing clump. But these effects depend strong-ly on the presence of heavy elements in thegas, and therefore they should be less im-portant for the earliest stars. Thus, it

seems safe to conclude that the first starsin the universe were typically many timesmore massive and luminous than the sun.

The Cosmic RenaissanceWHAT EFFECTS did these first starshave on the rest of the universe? An im-portant property of stars with no metalsis that they have higher surface tempera-tures than stars with compositions likethat of the sun. The production of nu-clear energy at the center of a star is lessefficient without metals, and the starwould have to be hotter and more com-pact to produce enough energy to coun-teract gravity. Because of the more com-pact structure, the surface layers of thestar would also be hotter. In collabora-tion with Rolf-Peter Kudritzki of the Uni-versity of Hawaii and Loeb of Harvard,one of us (Bromm) devised theoreticalmodels of such stars with masses between100 and 1,000 solar masses. The models


RICHARD B. LARSON and VOLKER BROMM have worked together to understand the pro-cesses that ended the “cosmic dark ages” and brought about the birth of the first stars. Lar-son, a professor of astronomy at Yale University, joined the faculty there in 1968 after re-ceiving his Ph.D. from the California Institute of Technology. His research interests includethe theory of star formation as well as the evolution of galaxies. Bromm earned his Ph.D.at Yale in 2000 and is now a postdoctoral researcher at the Harvard-Smithsonian Center forAstrophysics, where he focuses on the emergence of cosmic structure. The authors ac-knowledge the many contributions of Paolo Coppi, associate professor of astronomy at Yale,to their joint work on the formation of the first stars.

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It seems safe to conclude that the first stars in the universe were typically many times more

massive and luminous than the sun.


showed that the stars had surface tem-peratures of about 100,000 kelvins—

about 17 times higher than the sun’s sur-face temperature. Therefore, the first star-light in the universe would have beenmainly ultraviolet radiation from veryhot stars, and it would have begun to heatand ionize the neutral hydrogen and he-lium gas around these stars soon afterthey formed.

We refer to this event as the cosmicrenaissance. Although astronomers can-not yet estimate how much of the gas inthe universe condensed into the firststars, even a fraction as small as one partin 100,000 could have been enough forthese stars to ionize much of the remain-ing gas. Once the first stars started shin-ing, a growing bubble of ionized gaswould have formed around each star. Asmore and more stars began to form overmany hundreds of millions of years, thebubbles of ionized gas would have even-tually merged, and the intergalactic gas

would have become completely ionized.Scientists from the California Insti-

tute of Technology and the Sloan DigitalSky Survey have recently found evidencefor the final stages of this ionization pro-cess. The researchers observed strong ab-sorption of ultraviolet light in the spec-tra of quasars that date from about 900million years after the big bang. The re-sults suggest that the last patches of neu-tral hydrogen gas were being ionized atthat time. Helium requires more energyto ionize than hydrogen does, but if thefirst stars were as massive as predicted,they would have ionized helium at thesame time. On the other hand, if the firststars were not quite so massive, the heli-um must have been ionized later by en-ergetic radiation from sources such asquasars. Future observations of distantobjects may help determine when theuniverse’s helium was ionized.

If the first stars were indeed very mas-sive, they would also have had relatively

short lifetimes—only a few million years.Some of the stars would have exploded assupernovae at the end of their lives, ex-pelling the metals they produced by fu-sion reactions. Stars that are between 100and 250 times as massive as the sun arepredicted to blow up completely in ener-getic explosions, and some of the firststars most likely had masses in this range.Because metals are much more effectivethan hydrogen in cooling star-formingclouds and allowing them to collapse intostars, the production and dispersal ofeven a small amount could have had amajor effect on star formation.

Working in collaboration with An-drea Ferrara of the University of Flo-rence in Italy, we have found that whenthe abundance of metals in star-formingclouds rises above one thousandth of themetal abundance in the sun, the metalsrapidly cool the gas to the temperature ofthe cosmic background radiation. (Thistemperature declines as the universe ex-


Computer simulations have given scientists some indication of the possible masses, sizes and other characteristicsof the earliest stars. The lists below compare the best estimates for the first stars with those for the sun.

SUNMASS: 1.989 × 1030 kilogramsRADIUS: 696,000 kilometersLUMINOSITY: 3.85 × 1023 kilowattsSURFACE TEMPERATURE: 5,780 kelvinsLIFETIME: 10 billion years

FIRST STARSMASS: 100 to 1,000 solar massesRADIUS: 4 to 14 solar radiiLUMINOSITY: 1 million to 30 million solar unitsSURFACE TEMPERATURE: 100,000 to 110,000 kelvinsLIFETIME: 3 million years

COMPARING CHARACTERISTICS

STAR STATS


pands, falling to 19 kelvins a billionyears after the big bang and to 2.7kelvins today.) This efficient cooling al-lows the formation of stars with smallermasses and may also considerably boostthe overall rate at which stars are born.In fact, it is possible that the pace of starformation did not accelerate until afterthe first metals had been produced. Inthis case, the second-generation starsmight have been the ones primarily re-sponsible for lighting up the universe andbringing about the cosmic renaissance.

At the start of this active period ofstar birth, the cosmic background tem-perature would have been higher than

the temperature in present-day molecu-lar clouds (10 kelvins). Until the temper-ature dropped to that level—which hap-pened about two billion years after thebig bang—the process of star formationmay still have favored massive stars. Asa result, large numbers of such stars mayhave formed during the early stages ofgalaxy building by successive mergers ofprotogalaxies. A similar phenomenonmay occur in the modern universe whentwo galaxies collide and trigger a star-burst—a sudden increase in the rate ofstar formation. Such events are now fair-ly rare, but some evidence suggests thatthey may produce relatively large num-bers of massive stars.

Puzzling EvidenceTHIS HYPOTHESIS about early starformation might help explain some puz-zling features of the present universe. Oneunsolved problem is that galaxies containfewer metal-poor stars than would be ex-pected if metals were produced at a rateproportional to the star formation rate.This discrepancy might be resolved if ear-ly star formation had produced relative-ly more massive stars; on dying, thesestars would have dispersed large amountsof metals, which would have then beenincorporated into most of the low-massstars that we now see.

Another puzzling feature is the highmetal abundance of the hot x-ray-emit-ting intergalactic gas in clusters of galax-ies. This observation could be accountedfor most easily if there had been an earlyperiod of rapid formation of massivestars and a correspondingly high super-nova rate that chemically enriched the in-tergalactic gas. The case for a high super-nova rate at early times also dovetailswith the recent evidence suggesting thatmost of the ordinary matter and metals inthe universe lies in the diffuse intergalac-tic medium rather than in galaxies. Toproduce such a distribution of matter,galaxy formation must have been a spec-

tacular process, involving intense burstsof massive star formation and barrages ofsupernovae that expelled most of the gasand metals out of the galaxies.

Stars that are more than 250 timesmore massive than the sun do not explodeat the end of their lives; instead they col-lapse into similarly massive black holes.Several of the computer simulations men-tioned above predict that some of the firststars would have had masses this great.Because the first stars formed in the dens-est parts of the universe, any black holesresulting from their collapse would havebecome incorporated, via successive merg-ers, into systems of larger and larger size.It is possible that some of these black holesbecame concentrated in the inner part oflarge galaxies and seeded the growth ofthe supermassive black holes—millions oftimes more massive than the sun—that arenow found in galactic nuclei.

Furthermore, astronomers believe that

the energy source for quasars is the gaswhirling into the black holes at the cen-ters of large galaxies. If smaller blackholes had formed at the centers of someof the first protogalaxies, the accretion ofmatter into the holes might have gener-ated “mini quasars.” Because these ob-jects could have appeared soon after thefirst stars, they might have provided anadditional source of light and ionizingradiation at early times.

Thus, a coherent picture of the uni-verse’s early history is emerging, althoughcertain parts remain speculative. The for-mation of the first stars and protogalax-ies began a process of cosmic evolution.

Much evidence suggests that the periodof most intense star formation, galaxybuilding and quasar activity occurred afew billion years after the big bang andthat all these phenomena have continuedat declining rates as the universe hasaged. Most of the cosmic structure build-ing has now shifted to larger scales asgalaxies assemble into clusters.

In the coming years, researchers hopeto learn more about the early stages of thestory, when structures started developingon the smallest scales. Because the firststars were most likely very massive andbright, instruments such as the Next Gen-eration Space Telescope—the plannedsuccessor to the Hubble Space Tele-scope—might detect some of these an-cient bodies. Then astronomers may beable to observe directly how a dark, fea-tureless universe formed the brilliantpanoply of objects that now give us lightand life.


Second-generation stars might have beenprimarily responsible for the cosmic renaissance.

Before the Beginning: Our Universe and Others. Martin J. Rees. Perseus Books, 1998.

The Formation of the First Stars. Richard B. Larson in Star Formation from the Small to the Large Scale. Edited by F. Favata, A. A. Kaas and A. Wilson. ESA Publications, 2000. Available on the Web at www.astro.yale.edu/larson/papers/Noordwijk99.pdf

In the Beginning: The First Sources of Light and the Reionization of the Universe. R. Barkana and A. Loeb in Physics Reports, Vol. 349, No.2, pages 125–238; July 2001. Available on the Web at aps.arxiv.org/abs/astro-ph/0010468

Graphics from computer simulations of the formation of the first stars can be found atwww.tomabel.com



By Guinevere Kauffmann and Frank van den Bosch

Life Cycle

SOMBRERO GALAXY is an all-in-one package: it exemplifies nearly everygalactic phenomenon that astronomers have struggled for a century toexplain. It has a bright ellipsoidal bulge of stars, a supermassive black holeburied deep within that bulge, a disk with spiral arms (seen close to edge-on), and star clusters scattered about the outskirts. Stretching beyond thisimage is thought to be a vast halo of inherently invisible dark matter.

The

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Astronomers are on the verge of explaining the enigmatic variety of galaxies

GalaxiesofCOPYRIGHT 2002 SCIENTIFIC AMERICAN, INC.

14 S C I E N T I F I C A M E R I C A N U p d a t e d f r o m t h e J u n e 2 0 0 2 i s s u e

a mighty empire dooms itself through its hubris: it presumesto conquer and rule an entire galaxy. That seems a lofty ambi-tion indeed. To bring our Milky Way galaxy to heel, an empirewould have to vanquish 100 billion stars. But cosmologists—

those astronomers who study the universe as a whole—areunimpressed. The Milky Way is one of 50 billion or moregalaxies within the observable reaches of space. To conquer itwould be to conquer an insignificant speck.

A century ago nobody knew all those galaxies even existed.Most astronomers thought that the galaxy and the universewere synonymous. Space contained perhaps a billion stars, in-terspersed with fuzzy splotches that looked like stars in the pro-cess of forming or dying. Then, in the early decades of the 20thcentury, came the golden age of astronomy, when American as-tronomer Edwin Hubble and others determined that thosefuzzy splotches were often entire galaxies in their own right.

Why do stars reside in gigantic agglomerations separated byvast voids, and how do galaxies take on their bewildering vari-ety of shapes, sizes and masses? These questions have consumedastronomers for decades. It is not possible for us to observe agalaxy forming; the process is far too slow. Instead researchershave to piece the puzzle together by observing many differentgalaxies, each caught at a different phase in its evolutionary his-tory. Such measurements did not become routine until about

a decade ago, when astronomy entered a new golden age.Spectacular advances in telescope and detector technology

are now giving astronomers a view of how galaxies havechanged over cosmic timescales. The Hubble Space Telescopehas taken very deep snapshots of the sky, revealing galaxiesdown to unprecedentedly faint levels. Ground-based instru-ments such as the giant Keck telescopes have amassed statisticson distant (and therefore ancient) galaxies. It is as if evolution-ary biologists had been handed a time machine, allowing themto travel back into prehistory and take pictures of the animalsand plants inhabiting the earth at a series of different epochs.The challenge for astronomers, as it would be for the biologists,is to determine how the species observed at the earliest timesevolved into what we know today.

The task is of truly astronomical proportions. It involvesphysics on wildly disparate scales, from the cosmological evo-lution of the entire universe to the formation of a single star.That makes it difficult to build realistic models of galaxy for-mation, yet it brings the whole subject full circle. The discov-ery of all those billions of galaxies made stellar astronomy andcosmology seem mutually irrelevant. In the grand scheme ofthings, stars were just too small to matter; conversely, debatesover the origin of the universe struck most stellar astronomersas hopelessly abstract. Now we know that a coherent pictureof the universe must take in both the large and the small.

Galactic SpeciesTO UNDERSTAND HOW galaxies form, astronomers look forpatterns and trends in their properties. According to the classi-fication scheme developed by Hubble, galaxies may be broadlydivided into three major types: elliptical, spiral and irregular [seeillustration on opposite page]. The most massive ones are the el-lipticals. These are smooth, featureless, almost spherical systemswith little or no gas or dust. In them, stars buzz around the cen-ter like bees around a hive. Most of the stars are very old.

Spiral galaxies, such as our own Milky Way, are highly flat-tened and organized structures in which stars and gas move oncircular or near-circular orbits around the center. In fact, theyare also known as disk galaxies. The pinwheel-like spiral armsare filaments of hot young stars, gas and dust. At their centers,spiral galaxies contain bulges—spheroidal clumps of stars thatare reminiscent of miniature elliptical galaxies. Roughly a thirdof spiral galaxies have a rectangular structure toward the cen- E

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One of the liveliest subfields of astrophysics right now isthe study of how galaxies take shape. Telescopes areprobing the very earliest galaxies, and computersimulations can track events in unprecedented detail.

Researchers may soon do for galaxies what they did forstars in the early 20th century: provide a unifiedexplanation, based on a few general processes, for a hugediversity of celestial bodies. For galaxies, thoseprocesses include gravitational instability, radiativecooling and star formation, relaxation (galaxies reachinternal equilibrium) and interactions among galaxies.

Several vexing questions remain, however. A possibleanswer to these questions is that supernova explosionsactually have a profound and pervasive effect on their structure.

Overview/Galaxy Evolution

In many science-fiction stories,


TYPES OF GALAXIESASTRONOMERS SORT GALAXIES using the “tuning fork” classification schemedeveloped by American astronomer Edwin Hubble in the 1920s. According tothis system, galaxies come in three basic types: elliptical (represented by thehandle of the fork at right), spiral (shown as prongs) and irregular (shownbelow at left). The smallest galaxies, known as dwarfs, have their ownuncertain taxonomy.

Within each of the types are subtypes that depend on the details of thegalaxy’s shape. Going from the top of the tuning fork to the bottom, the galacticdisk becomes more prominent in optical images and the central bulge less so.The different Hubble types may represent various stages of development.Galaxies start off as spirals without bulges, undergo a collision during whichthey appear irregular, and end up as ellipticals or as spirals with bulges.

—G.K. and F.v.d.B.

ELLIPTICALS

M89E0

M84S0

M49E4

M110E5

NGC 660SBa

NGC 7479SBb

M58SBc

NGC 4622Sb

M51Sc

NGC 7217Sa

Leo ISpheroidal

M82Irregular

VII Zw 403Blue Compact

M32Elliptical

Small Magellanic CloudIrregular

IRREGULARS

N . A . S H A R P / N O A O / A U R A / N S F ( M 8 2 ) ; B . K E E L / H A L L T E L E S C O P E / L O W E L L O B S E R V A T O R Y ( M 3 2 ) ; R . S C H U L T E - L A D B E C K / U . H O P P / M . C R O N E / A S T R O P H Y S I C A L J O U R N A L ( b l u e c o m p a c t d w a r f ) ;N O A O / A U R A / N S F ( S m a l l M a g e l l a n i c C l o u d ) ; D A V I D M A L I N , © A N G L O - A M E R I C A N O B S E R V A T O R Y ( L e o I ) ; N O A O / A U R A / N S F ( M 8 9 , M 4 9 , M 1 1 0 , M 8 4 ) ; R . B R A N C H / R . M I L N E R / A . B L O C K / N O A O /A U R A / N S F ( N G C 6 6 0 ) ; A . B L O C K / N O A O / A U R A / N S F ( N G C 7 4 7 9 ) ; F . C I E S L A K / A . B L O C K / N O A O / A U R A / N S F ( M 5 8 ) ; B . K E E L / R . B U T A / G . P U R C E L L / C E R R O T O L O L O I N T E R - A M E R I C A N O B S E R V A T O R Y ,C H I L E ( N G C 7 2 1 7 ) ; G . B Y R D / R . B U T A / T . F R E E M A N / N A S A ( N G C 4 6 2 2 ) ; N A S A / S T S C I / A U R A ( M 5 1 )

NORMAL SPIRALS

DWARF TYPES

BARRED SPIRALS


ter. Such “bars” are thought to arise from instabilities in the disk.Irregular galaxies are those that do not fit into the spiral or

elliptical classifications. Some appear to be spirals or ellipticalsthat have been violently distorted by a recent encounter witha neighbor. Others are isolated systems that have an amor-phous structure and exhibit no signs of any recent disturbance.

Each of these three classes covers galaxies with a wide rangeof luminosities. On average, however, ellipticals are brighterthan spirals, and fainter galaxies are more likely than their lu-minous counterparts to be irregular. For the faintest galaxies,the classification scheme breaks down altogether. These dwarfgalaxies are heterogeneous in nature, and attempts to pigeon-hole them have proved controversial. Loosely speaking, they fallinto two categories: gas-rich systems where stars are activelyforming and gas-poor systems where no stars are forming.

An important clue to the origin of the galaxy types comesfrom the striking correlation between type and local galaxy den-sity. Most galaxies are scattered through space far from theirnearest neighbor, and of these only 10 to 20 percent are ellipti-cals; spirals dominate. The remaining galaxies, however, arepacked into clusters, and for them the situation is reversed. El-lipticals are the majority, and the spirals that do exist are ane-mic systems depleted of gas and young stars. This so-called mor-phology-density relation has long puzzled astronomers.

Light and DarkA SMALL PERCENTAGE of spirals and ellipticals are pecu-liar in that they contain an exceedingly luminous, pointlikecore—an active galactic nucleus (AGN). The most extreme andrarest examples are the quasars, which are so bright that theycompletely outshine their host galaxies. Astronomers general-ly believe that AGNs are powered by black holes weighing mil-lions to billions of solar masses. Theory predicts that gas fallinginto these monsters will radiate about 10 percent of its intrin-sic energy, sufficient to generate a beacon that can be detectedon the other side of the universe.

Once considered anomalies, AGNs have recently beenshown to be integral to the process of galaxy formation. Thepeak of AGN activity occurred when the universe was ap-proximately a fourth of its present age—the same time thatmost of the stars in ellipticals were being formed. Furthermore,supermassive black holes are now believed to reside in virtual-ly every elliptical galaxy, as well as every spiral galaxy that hasa bulge, regardless of whether those galaxies contain an AGN[see “The Hole Shebang,” by George Musser; News and Analy-sis, Scientific American, October 2000]. The implication is

that every galaxy may go through one or more episodes ofAGN activity. As long as matter falls into the black hole, thenucleus is active. When no new material is supplied to the cen-ter, it lies dormant.

Most of the information we have about all these phenom-ena comes from photons: optical photons from stars, radiophotons from neutral hydrogen gas, x-ray photons from ion-ized gas. But the vast majority of the matter in the universe maynot emit photons of any wavelength. This is the infamous darkmatter, whose existence is inferred solely from its gravitation-al effects. The visible parts of galaxies are believed to be en-veloped in giant “halos” of dark matter. These halos, unlikethose found above the heads of saints, have a spherical or el-lipsoidal shape. On larger scales, analogous halos are thoughtto keep clusters of galaxies bound together.

Unfortunately, no one has ever detected dark matter di-rectly, and its nature is still one of the biggest mysteries in sci-ence. Currently most astronomers favor the idea that dark mat-ter consists mostly of hitherto unidentified particles that bare-ly interact with ordinary particles or with one another.Astronomers typically refer to this class of particles as cold darkmatter (CDM) and any cosmological model that postulatestheir existence as a CDM model.

Over the past two decades, astronomers have painstaking-ly developed a model of galaxy formation based on CDM. Thebasic framework is the standard big bang theory for the expan-sion of the universe. Cosmologists continue to debate how theexpansion got going and what transpired early on, but these un-certainties do not matter greatly for galaxy formation. We pickup the story about 100,000 years after the big bang, when theuniverse consisted of baryons (that is, ordinary matter, pre-dominantly hydrogen and helium nuclei), electrons (bound tothe nuclei), neutrinos, photons and CDM. Observations indi-cate that the matter and radiation were distributed smoothly:


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GUINEVERE KAUFFMANN and FRANK VAN DEN BOSCH are re-searchers at the Max Planck Institute for Astrophysics in Garch-ing, Germany. They are among the world’s experts on the theo-retical modeling of galaxy formation. Kauffmann has recentlyturned her attention to analyzing data from the Sloan Digital SkySurvey, which she believes holds the answers to some of the mys-teries highlighted in this article. In her spare time, she enjoys ex-ploring Bavaria with her son, Jonathan. Van den Bosch is partic-ularly intrigued by the formation of disk galaxies and of massiveblack holes in galactic centers. In his free time, he can often befound in a Munich beer garden.

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Supercomputer simulations of the spatial distribution

of galaxies are in excellent agreement

with observations.



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3Eventually these patches become sodense, relative to their surroundings,

that gravity takes over from expansion. The patches start to collapse.

COOKING UP A GALAXY

4As each patch collapses, it attainsequilibrium. The density, both of

ordinary and of dark matter, peaks at thecenter and decreases toward the edge.

5Dark matter, being unable to radiate,retains this shape. But ordinary matter

emits radiation, collapses into a rotatingdisk and begins to condense into stars.

2At first, cosmic expansion overpowersgravity. The fluid thins out. But patches

of higher density thin out more slowly thanother regions do.

1In the beginning, a primordial fluid—amixture of ordinary matter (blue) and

dark matter (red)—fills the universe. Itsdensity varies subtly from place to place.

7When two disks of similar size merge,the stellar orbits become scrambled.

An elliptical galaxy results. Later a diskmay develop around the elliptical.

8The merger triggers new star formationand feeds material into the central

black hole, generating an active galacticnucleus, which can spew plasma jets.

6Protogalaxies interact, exertingtorques on one another and merging

to form larger and larger bodies. (This stepoverlaps with steps 4 and 5.)

THREE BASIC PROCESSES dictated howthe primordial soup congealed intogalaxies: the overall expansion of theuniverse in the big bang, the force ofgravity, and the motion of particles andlarger constituents. The shifting balanceamong these processes can explain whygalaxies became discrete, coherentbodies rather than a uniform gas or ahorde of black holes. In this theory, smallbodies coalesce first and then glomtogether to form larger objects. A crucialingredient is dark matter, which reachesa different equilibrium than ordinarymatter. —G.K. and F.v.d.B.

Radiation


the density at different positions varied by only about one partin 100,000. The challenge is to trace how these simple ingredi-ents could give rise to the dazzling variety of galaxies.

If one compares the conditions back then with the distribu-tion of matter today, two important differences stand out. First,the present-day universe spans an enormous range of densities.The central regions of galaxies are more than 100 billion timesas dense as the universe on average. The earth is another 10 bil-lion billion times as dense as that. Second, whereas the baryonsand CDM were initially well mixed, the baryons today formdense knots (the galaxies) inside gargantuan halos of dark mat-ter. Somehow the baryons have decoupled from the CDM.

The first of these differences can be explained by the processof gravitational instability. If a region is even slightly more densethan average, the excess mass will exert a slightly stronger-than-average gravitational force, pulling extra matter toward itself.This creates an even stronger gravitational field, pulling in evenmore mass. This runaway process amplifies the initial densitydifferences.

Sit Back and RelaxALL THE WHILE, the gravity of the region must compete withthe expansion of the universe, which pulls matter apart. Initial-ly cosmic expansion wins and the density of the region de-creases. The key is that it decreases more slowly than the densi-ty of its surroundings. At a certain point, the overdensity of theregion compared with its surroundings becomes so pronouncedthat its gravitational attraction overcomes the cosmic expan-sion. The region starts to collapse.

Up to this point, the region is not a coherent object but mere-ly a random enhancement of density in the haze of matter that

fills the universe. But once the region collapses, it starts to takeon an internal life of its own. The system—which we shall calla protogalaxy from here on—seeks to establish some form ofequilibrium. Astronomers refer to this process as relaxation. Thebaryons behave like the particles of any gas. Heated by shockwaves that are triggered by the collapse, they exchange energythrough direct collisions with one another, thus achieving hy-drostatic equilibrium—a state of balance between pressure andgravity. The earth’s atmosphere is also in hydrostatic equilibri-um (or nearly so), which is why the pressure decreases expo-nentially with altitude.

For the dark matter, however, relaxation is distinctively dif-ferent. CDM particles are, by definition, weakly interactive; theyare not able to redistribute energy among themselves by directcollisions. A system of such particles cannot reach hydrostaticequilibrium. Instead it undergoes what is called, perhaps oxy-moronically, violent relaxation. Each particle exchanges ener-gy not with another individual particle but with the collectivemass of particles, by way of the gravitational field.

Bodies traveling in a gravitational field are always undergo-ing an exchange of gravitational and kinetic energy. If youthrow a ball into the air, it rises to a higher altitude but decel-erates: it gains gravitational energy at the expense of kinetic en-ergy. On the way down, the ball gains kinetic energy at the ex-pense of gravitational energy. CDM particles in a protogalaxybehave much the same way. They move around and changespeed as their balance of gravitational and kinetic energy shifts.But unlike balls near the earth’s surface, CDM particles movein a gravitational field that is not constant. After all, the grav-itational field is produced by all the particles together, whichare undergoing collapse.


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GALACTIC DENSITY VARIATIONSDENSITY VARIATIONS in the pregalactic universe followed apattern that facilitated the formation of protogalaxies. Thevariations were composed of waves of various wavelengths. A small wave was superimposed on a slightly larger wave,

which was superimposed on an even larger wave, and so on.Therefore, the highest density occurred over the smallestregions. These regions collapsed first and became the buildingblocks for larger structures. —G.K. and F.v.d.B.

Position

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Regions thatcollapse first


Changes in the gravitational field cause some particles togain energy and others to lose energy. Just as for the baryons,this redistribution of the energies of the particles allows the sys-tem to relax, forming a CDM halo that is said to be in virialequilibrium. The process is complicated and has never beenworked out in great theoretical detail. Instead researchers trackit using numerical simulations, which show that all CDM halosin virial equilibrium have similar density profiles.

The end point of the collapse and relaxation of a proto-galaxy is a dark matter halo, inside of which the baryonic gasis in hydrostatic equilibrium at a temperature of typically a fewmillion degrees. Whereas each CDM particle conserves its en-ergy from then on, the baryonic gas is able to emit radiation. Itcools, contracts and accumulates at the center of the dark mat-ter halo. Cooling, therefore, is the process responsible for de-coupling the baryons from the CDM.

So far we have focused on a single protogalaxy and ignoredits surroundings. In reality, other protogalaxies will form near-by. Gravity will pull them together until they merge to form agrander structure. This structure will itself merge, and so on. Hi-erarchical buildup is a characteristic feature of CDM models.The reason is simple. Because small-scale fluctuations in densi-ty are superimposed on larger-scale fluctuations, the densityreaches its highest value over the smallest regions. An analogyis the summit of a mountain. The exact position of the peak cor-responds to a tiny structure: for example, a pebble on top of arock on top of a hill on top of the summit. If a cloud bank de-scends on the mountain, the pebble vanishes first, followed bythe rock, the hill and eventually the whole mountain.

Similarly, the densest regions of the early universe are thesmallest protogalaxies. They are the first regions to collapse, fol-lowed by progressively larger structures. What distinguishesCDM from other possible types of dark matter is that it has den-sity fluctuations on all scales. Neutrinos, for example, lack fluc-tuations on small scales. A neutrino-dominated universe wouldbe like a mountain with an utterly smooth summit.

The hierarchical formation of dark matter halos cannot bedescribed using simple mathematical relationships. It is beststudied using numerical simulations. To emulate a represen-tative part of the universe with enough resolution to see the for-mation of individual halos, researchers must use the latest su-percomputers. The statistical properties and spatial distribu-tion of the halos emerging from these simulations are inexcellent agreement with those of observed galaxies, providingstrong support for the hierarchical picture and hence for the ex-istence of CDM.

Take a SpinTHE HIERARCHICAL PICTURE naturally explains theshapes of galaxies. In spiral galaxies, stars and gas move on cir-cular orbits. The structure of these galaxies is therefore governedby angular momentum. Where does this angular momentumcome from? According to the standard picture, when proto-galaxies filled the universe, they exerted tidal forces on one an-other, causing them to spin. After the protogalaxies collapsed,each was left with a net amount of angular momentum.

When the gas in the protogalaxies then started to cool, it con-tracted and started to fall toward the center. Just as ice-skatersspin faster when they pull in their arms, the gas rotated faster andfaster as it contracted. The gas thus flattened out, in the same waythat the earth is slightly flatter than a perfect sphere because ofits rotation. Eventually the gas was spinning so fast that the cen-trifugal force (directed outward) became equal to the gravita-tional pull (directed inward). By the time the gas attained cen-trifugal equilibrium, it had flattened into a thin disk. The diskwas sufficiently dense that the gas started to clump into theclouds, out of which stars then formed. A spiral galaxy was born.

Because most dark matter halos end up with some angularmomentum, one has to wonder why all galaxies aren’t spirals.How did ellipticals come into being? Astronomers have long heldtwo competing views. One is that most of the stars in present-dayellipticals and bulges formed during a monolithic collapse at ear-ly epochs. The other is that ellipticals are relative latecomers, hav-ing been produced as a result of the merging of spiral galaxies.

The second view has come to enjoy increasing popularity. De-tailed computer simulations of the merger of two spirals showthat the strongly fluctuating gravitational field destroys the twodisks. The stars within the galaxies are too spread out to bang intoone another, so the merging process is quite similar to the violentrelaxation suffered by dark matter. If the galaxies are of compa-rable mass, the result is a smooth clump of stars with propertiesthat strongly resemble an elliptical. Much of the gas in the twooriginal disk galaxies loses its angular momentum and plummetstoward the center. There the gas reaches high densities and startsto form stars at a frenzied rate. At later times, new gas may fall in,cool off and build up a new disk around the elliptical. The resultwill be a spiral galaxy with a bulge in the middle.

The high efficiency of star formation during mergers ex-plains why ellipticals typically lack gas: they have used it up.The merger model also accounts for the morphology-densityrelation: a galaxy in a high-density environment will undergomore mergers and is thus more likely to become an elliptical.

Observational evidence confirms that mergers and inter-


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Astronomers may be directly observing,

for the first time, the formation of

elliptical galaxies.


actions have been common in the universe, particularly earlyon. In Hubble Space Telescope images, many ancient galaxieshave disturbed morphologies, a telltale sign of interaction.Moreover, the number of starburst galaxies—in which starsform at a frenetic pace—increases dramatically at earlier times.Astronomers may be directly observing, for the first time, theformation of elliptical galaxies.

If elliptical galaxies and spiral bulges are linked to galaxymergers, then it follows that supermassive black holes may becreated in these events, too. Hole masses are strongly correlat-ed with the mass of the surrounding elliptical galaxy or bulge;they are not correlated with the mass of the spiral disk. Merg-er models have been extended to incorporate supermassiveholes and therefore AGNs. The abundant gas that is funneledtoward the center during a merger could revive a dormant

black hole. In other words, quasars were more common in thepast because mergers were much more common then.

As for dwarf galaxies, in the hierarchical picture they arethe leftovers—small clumps that have yet to merge. Recent ob-servations show that star formation in dwarfs is particularly er-ratic, coming in short bursts separated by long quiescent peri-ods [see “Dwarf Galaxies and Starbursts,” by Sara C. Beck;Scientific American, June 2000]. In heftier galaxies such asthe Milky Way, star formation occurs at a more constant rate.These results are intriguing because astronomers have often hypothesized that the mass of a galaxy determines its fertility.In lightweight galaxies, supernova explosions can easily disruptor even rid the system of its gas, thus choking off star forma-tion. Even the smallest perturbation can have a dramatic effect.It is this sensitivity to initial conditions and random events


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HOW RELAXING

1Initially the dark matter has the samearrangement as ordinary matter. The

difference is that particles do not collide.2As the particles move around, the

gravitational field changes, whichcauses particles to gain or lose energy.

3Gradually the system settles down intovirial equilibrium, in which the

gravitational field no longer fluctuates.

1The ordinary matter—predominantlyhydrogen gas—starts off moving every

which way. Its density varies randomly.2The gas particles bang into one

another, redistributing energy andgenerating a pressure that resists gravity.

3Eventually the gas settles down intohydrostatic equilibrium, with the

density highest near the center of gravity.

GRAVITY CAUSES small density perturbations to grow until theyfinally start to collapse. During the collapse the gas and darkmatter seek to establish an internal state of equilibrium. This

equilibrium determines the overall properties of the galaxy, such asits shape and density profile. The ordinary matter and dark matterattain equilibrium by different means. —G.K. and F.v.d.B.

Ordinary matter

Dark matter


that may account for the heterogeneity of the galactic dwarfs.Although the standard picture of galaxy formation is re-

markably successful, researchers are still far from working outall the processes involved. Moreover, they have yet to resolvesome troubling inconsistencies. The simple picture of gas cool-ing inside dark matter halos faces an important problem knownas the cooling catastrophe. Calculations of the cooling rates im-ply that the gas should have cooled briskly and pooled in the cen-ters of halos, leaving intergalactic space virtually empty. Yet thespace between galaxies is far from empty. Some extra input ofenergy must have prevented the gas from cooling down.

Some Feedback, PleaseANOTHER PROBLEM CONCERNS angular momentum. Theamount of angular momentum imparted to protogalaxies in themodels is comparable to the angular momentum that we actu-ally see in spiral galaxies. So long as the gas retains its angularmomentum, the CDM picture reproduces the observed sizes ofspirals. Unfortunately, in the simulations the angular momen-tum leaks away. Much of it is transferred to the dark matter dur-ing galaxy mergers. As a result, the disks emerging from thesesimulations are a factor of 10 too small. Apparently the mod-els are still missing an essential ingredient.

A third inconsistency has to do with the number of dwarfgalaxies. Hierarchical theories predict a proliferation of low-mass dark matter halos and, by extension, dwarf galaxies. Theseare simply not seen. In the neighborhood of the Milky Way, thenumber of low-mass dwarfs is a factor of 10 to 100 lower thantheories predict. Either these dark matter halos do not exist orthey are present but have eluded detection because stars do notform within them.

Several solutions have been suggested for these problems.The proposals fall into two classes: either a fundamental changeto the model, perhaps to the nature of dark matter [see “What’sthe Matter?” by George Musser; News and Analysis, Scien-tific American, May 2000], or a revision of our picture ofhow the cooling gas is transformed into stars. Because most as-tronomers are reluctant to abandon the CDM model, whichworks so well on scales larger than galaxies, they have concen-trated on improving the treatment of star formation. Currentmodels gloss over the process, which occurs on scales that aremuch smaller than a typical galaxy. Incorporating it in full is farbeyond the capabilities of today’s supercomputers.

Yet star formation can have profound effects on the struc-ture of a galaxy [see “The Gas between the Stars,” by RonaldJ. Reynolds; Scientific American, January 2002]. Some as-

tronomers think that the action of stars might actually solve allthree problems at once. The energy released by stars can heatthe gas, obviating the cooling catastrophe. Heating also slowsthe descent of gas toward the center of the galaxy and therebyreduces its tendency to transfer angular momentum to the darkmatter—alleviating the angular momentum problem. And su-pernova explosions could expel mass from the galaxies backinto the intergalactic medium [see “Colossal Galactic Explo-sions,” by Sylvain Veilleux, Gerard Cecil and Jonathan Bland-Hawthorn; Scientific American, February 1996]. For thelowest-mass halos, whose escape velocity is small, the processcould be so efficient that hardly any stars form, which wouldexplain why we observe fewer dwarf galaxies than predicted.

Because our understanding of these processes is poor, themodels still have a lot of wiggle room. It remains to be seenwhether the problems really can be fixed or whether they indi-cate a need for a completely new framework. Our theory ofgalaxy formation will surely continue to evolve. The observa-tional surveys under way, such as the Sloan Digital Sky Survey,will enormously improve the data on both nearby and distantgalaxies. Further advances in cosmology will help constrain theinitial conditions for galaxy formation. Already, precise obser-vations of the cosmic microwave background radiation havepinned down the values of the large-scale cosmological para-meters, freeing galactic modelers to focus on the small-scale in-tricacy. Soon we may unite the large, the small and the medi-um into a seamless picture of cosmic evolution.


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Cosmological Physics. John A. Peacock. Cambridge University Press, 1999.

The Formation of Ellipticals, Black Holes and Active Galactic Nuclei: A Theoretical Perspective. Guinevere Kauffmann, Stéphane Charlot andMartin G. Haehnelt in Philosophical Transactions of the Royal Society ofLondon, Series A, Vol. 358, No. 1772, pages 2121–2132; July 15, 2000.

The Big Bang. Joseph Silk. W. H. Freeman and Company, 2001.

The Morphological Evolution of Galaxies. Roberto G. Abraham andSidney van den Bergh in Science, Vol. 293, No. 5533, pages 1273–1278;August 17, 2001. Available at arxiv.org/abs/astro-ph/0109358

The Angular Momentum Content of Dwarf Galaxies: New Challenges for the Theory of Galaxy Formation. Frank C. van den Bosch, AndreasBurkert and Rob A. Swaters in Monthly Notices of the Royal AstronomicalSociety, Vol. 326, No. 3, pages 1205–1215; September 21, 2001.Available at astro-ph/0105082

New Perspectives in Astrophysical Cosmology. Martin Rees. Secondedition. Cambridge University Press, 2002.

Galaxy Formation and Evolution: Recent Progress. Richard S. Ellis.Lecture given at the XIth Canary Islands Winter School of Astrophysics,“Galaxies at High Redshift” (in press). Available at astro-ph/0102056


Supernova explosions could expel mass from low-mass

galaxies so efficiently that

hardly any stars would form.


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Exploding stars seen across immensedistances showthat the cosmicexpansion may beaccelerating–a signthat an exotic new form of energy could be driving the universe apart

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SUPERNOVAE

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By Craig J. Hogan, Robert P. Kirshner and Nicholas B. Suntzeff

WHERE’S THE SUPERNOVA? This pair of images, made bythe authors’ team using the four-meter-diameter BlancoTelescope at Cerro Tololo Inter-American Observatory inChile, provided the first evidence of one supernova. Inthe image at the right, obtained three weeks after theone at the left, the supernova visibly (but subtly) altersthe appearance of one of the galaxies. Can you find it?Some differences are caused by varying atmosphericconditions. To check, consult the key on page 28.P

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A long time ago (some five billion years),in a galaxy far, far away (about 2,000 megaparsecs), a long-dead star exploded with a flash brighter than a billion suns. Itslight spread out across space, fading and stretching with the ex-panding cosmos, before some of it finally reached the earth.Within 10 minutes during one dark night in 1997, a few hun-dred photons from this supernova landed on the mirror of a tele-scope in Chile. A computer at the observatory then created adigital image that showed the arrival of this tiny blip of light.Though not very impressive to look at, for us this faint spot wasa thrilling sight—a new beacon for surveying space and time.

We and our colleagues around the world have tracked thearrival of light from several dozen such supernovae and usedthese observations to map the overall shape of the universe andto chronicle its expansion. What we and another team of as-tronomers have recently discerned challenges decades of con-ventional wisdom: it seems the universe is bigger and emptierthan suspected. Moreover, its ongoing expansion is not slow-

ing down as much as many cosmologists had anticipated; infact, it may be speeding up.

Star WarpsTHE HISTORY OF COSMIC EXPANSION has been of keeninterest for nearly a century, because it reflects on both thegeometry of the universe and the nature of its constituents—

matter, light and possibly other, more subtle forms of energy.Einstein’s general theory of relativity knits together these fun-damental properties of the universe and describes how they af-fect the motion of matter and the propagation of light, therebyoffering predictions for concrete things that astronomers canactually measure.

Before the publication of Einstein’s theory in 1916 and thefirst observations of cosmic expansion during the followingdecade, most scientists thought the universe stayed the samesize. Indeed, Einstein himself distrusted his equations when herealized they implied a dynamic universe. But new measure-ments of galactic motions by Edwin P. Hubble and others left

no doubt: faint, distant galaxies were flying away from theearth faster than bright, nearby ones, matching the predictionsof general relativity for a universe that grows and carries galax-ies farther apart. These researchers determined the outward ve-locities of galaxies from the shift of visible spectral lines tolonger wavelengths (so-called redshifts). Though often ascribedto the Doppler effect—the phenomenon responsible for thechanging pitch of a passing train whistle or car horn—the cos-mological redshift is more correctly thought of as a result of theongoing expansion of the universe, which stretches the wave-length of light passing between galaxies. Emissions from moredistant objects, having traveled for a greater time, become moreredshifted than radiation from nearer sources.

The technology of Hubble’s day limited the initial probingof cosmic expansion to galaxies that were comparatively close.In the time it took light from these nearby galaxies to reach theearth, the universe had expanded by only a small fraction of its

overall size. For such modest changes, redshift is directly pro-portional to distance; the fixed ratio of the two is called Hub-ble’s constant and denotes the current rate of cosmic expan-sion. But astronomers have long expected that galaxies fartheraway would depart from this simple relation between redshiftand distance, either because the pace of expansion has changedover time or because the intervening space is warped. Measur-ing this effect thus constitutes an important goal for cosmolo-gists—but it is a difficult one, requiring the means to determinethe distances to galaxies situated tremendously far away.

Hubble and other pioneers estimated distances to variousgalaxies by assuming that they all had the same intrinsic bright-ness. According to their logic, the ones that appeared brightwere comparatively close, and the ones that appeared dim werefar away. But this methodology works only crudely, becausegalaxies differ in their properties. And it fails entirely for dis-tant sources—whose light takes so long to reach the earth thatit reveals the faraway galaxies as they were billions of years ago(that is, in their youth)—because their intrinsic brightness could


Distant supernovae are25 percent dimmer than was forecast, indicating an accelerating

expansion of space.


have been quite different from that of more mature galaxiesseen closer to home. It is difficult to disentangle these evolu-tionary changes from the effects of the expansion, so as-tronomers have long sought other “standard candles” whoseintrinsic brightness is better known.

To be visible billions of light-years away, these beaconsmust be very bright. During the early 1970s, some cosmic sur-veyors tried using quasars, which are immensely energeticsources (probably powered by black holes swallowing stars andgas). But the quasars they studied proved even more diversethan galaxies and thus were of little use.

About the same time, other astronomers began exploringthe idea of using supernovae—exploding stars—as standardcandles for cosmological studies. That approach was contro-versial because supernovae, too, show wide variation in theirproperties. But in the past decade research by members of ourteam has enabled scientists to determine the intrinsic brightnessof one kind of supernova—type Ia—quite precisely.

Death StarWHAT IS A TYPE IA SUPERNOVA? Essentially, it is the blastthat occurs when a dead star becomes a natural thermonuclearbomb. Spectacular as this final transformation is, the progeni-tor begins its life as an ordinary star, a stable ball of gas whoseouter layers are held up by heat from steady nuclear reactionsin its core, which convert hydrogen to helium, carbon, oxygen,neon and other elements. When the star dies, the nuclear ashescoalesce into a glowing ember, compressed by gravity to the sizeof the earth and a million times the density of ordinary matter.

Most such white dwarf stars simply cool and fade away, dy-ing with a whimper. But if one is orbiting near another star, itcan slurp up material from its companion and become denser

and denser until a runaway thermonuclear firestorm ignites. Thenuclear cataclysm blows the dwarf star apart, spewing out ma-terial at about 10,000 kilometers a second. The glow of this ex-panding fireball takes about three weeks to reach its maximumbrightness and then declines over a period of months.

These supernovae vary slightly in their brilliance, but thereis a pattern: bigger, brighter explosions last somewhat longerthan fainter ones. So by monitoring how long they last, as-tronomers can correct for the differences and deduce their in-herent brightness to within 12 percent. Over the past decadestudies of nearby type Ia supernovae with modern detectorshave made these flashes the best calibrated standard candlesknown to astronomers.

One of these candles lights up somewhere in a typicalgalaxy about once every 300 years. Although such stellar ex-plosions in our own Milky Way are rare celestial events, if youmonitor a few thousand other galaxies, you can expect thatabout one type Ia supernova will appear every month. Indeed,there are so many galaxies in the universe that, somewhere in


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COSMIC EXPANSION could, in theory, follow one of three simple patterns: it may be constant(left), decelerating (center) or accelerating (right). In each case, a given portion of the universegrows in size as time passes ( from bottom to top). But the age of the universe—the time elapsedsince the beginning of the expansion—is greater for an accelerating universe and less for adecelerating universe, compared with the constant expansion case.

CRAIG J. HOGAN, ROBERT P. KIRSHNER and NICHOLAS B. SUNTZEFFshare a long-standing interest in big things that go bang. Hoganearned his doctorate at the University of Cambridge and is profes-sor and vice provost for research at the University of Washington.Kirshner attained his Ph.D. at the California Institute of Technolo-gy, studying a type Ia supernova observed in 1972 (the brightestone seen since 1937). He is professor of astronomy at Harvard Uni-versity and also serves as associate director of the Harvard-Smith-sonian Center for Astrophysics. Suntzeff received his Ph.D. at theUniversity of California, Santa Cruz. He works at Cerro Tololo Inter-American Observatory in La Serena, Chile, and is made of elementsformed in supernovae more than five billion years ago.

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the sky, supernovae bright enough to study erupt every few sec-onds. All astronomers have to do is find them and study themcarefully. For the past few years, that effort has occupied bothour research group, dubbed the “High-Z Team” (for the let-ter that astronomers use to denote redshift), a loose affiliationorganized in 1995 by Brian P. Schmidt of Mount Stromlo andSiding Spring Observatories in Australia, and a competing col-laboration called the Supernova Cosmology Project, which be-gan in 1988 and is led by Saul Perlmutter of Lawrence Berke-ley National Laboratory.

Although the two teams have independent programs, theyare exploiting the same fundamental advance: the deploymentof large electronic light detectors on giant telescopes, a combi-nation that produces digital images of faint objects over sizableswaths of the sky. A prime example of this new technology (onethat has served both teams) is the Big Throughput Camera,which was developed by Gary M. Bernstein of the University ofMichigan and J. Anthony Tyson of Lucent Technologies. Whenthis camera is placed at the focus of the four-meter Blanco Tele-scope at Cerro Tololo Inter-American Observatory in Chile, asingle exposure covers an area about as big as the full moon andcreates a picture of about 5,000 galaxies in 10 minutes.

Finding distant supernovae is just a matter of taking imagesof the same part of the sky a few weeks apart and searching for

changes that might be exploding stars. Because the digital lightdetectors can count the number of photons in each picture ele-ment precisely, we simply subtract the first image from the sec-ond and look for significant differences from zero. Because weare checking thousands of galaxies in each image pair, we can beconfident that the search of multiple pairs will find many super-novae—as long as the weather is good. Fortunately, the locationof the observatory, in the foothills of the Andes on the southernfringe of Chile’s Atacama Desert (one of the driest places in theworld), usually provides clear skies. Betting that we will make

some good discoveries, we schedule observing time in advanceon a battery of other telescopes around the world so that follow-up measurements can start before the supernovae fade away.

In practice, the search for exploding stars in the heavenswhips up its own burst of activity on the ground, because wemust acquire and compare hundreds of large, digital imagesat a breakneck pace. We commandeer computers scatteredthroughout the Cerro Tololo observatory for the tasks of align-ing the images, correcting for differences in atmospheric trans-parency and image size, and subtracting the two scans. If allgoes well, most of the galaxies disappear, leaving just a little vi-sual “noise” in the difference of the two images. Larger sig-nals indicate some new or changing object, such as variablestars, quasars, asteroids—and in a few cases, supernovae.


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New maps of the cosmic background radiation suggest that

the universe is flat and filled with dark energy.

RUBBER-BAND EXPERIMENT shows thelinear relation between recessionvelocity and distance. Here twosnapshots are shown of a rubber bandpulled upward at a certain rate. The velocity of different points marked on the band is given by the length of thecolored arrows. For example, the pointclosest to the origin moves the leastduring the interval between snapshots,so its velocity is the smallest (yellowarrow). In contrast, the farthest pointmoves the most, so its velocity is thehighest (violet arrow). The slope of theresulting line is the rate of expansion (left graph). If the rate changes over time,the slope, too, will change (right graph).Earlier times plot toward the upper right,because light from more distant objectstakes longer to reach the earth, the originof the plot. If the rate was slower in thepast—indicating that the expansion hasbeen accelerating—the line will curveupward (red line). If the rate was faster—as in a decelerating expansion—it willcurve downward (blue line).

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Our software records the position of new objects and at-tempts to identify which are truly supernovae. But the auto-mated tests are imperfect, and we must scrutinize the imagesby eye to decide whether a putative supernova is real. Becausewe must immediately pursue our discoveries with other tele-scopes, the analysis must be done quickly. During these ex-hausting times, the observatory becomes a sweatshop of as-tronomers and visiting students, who work around the clock fordays at a stretch, sustained by enthusiasm and Chilean pizza.

We next target the best supernova candidates with thelargest optical instruments in the world, the Keck telescopesin Hawaii. These critical observations establish whether theobjects discovered are in fact type Ia supernovae, gauge theirintrinsic brightness more exactly and determine their redshifts.

On the Dark SideOTHERS IN OUR GROUP, working with telescopes in Aus-tralia, Chile and the U.S., also follow these supernovae to trackhow their brilliance peaks and then slowly fades. The observ-ing campaign for a single supernova spans months, and the fi-nal analysis often has to wait a year or more, when the light ofthe exploded star has all but disappeared, so we can obtain agood image of its host galaxy. We use this final view to subtractthe constant glow of the galaxy from the images of the super-nova. Our best measurements come from the Hubble SpaceTelescope, which captures such fine details that the explodingstar stands out distinctly from its host galaxy.

The two teams have now studied a total of a few scorehigh-redshift supernovae, ones that erupted between four bil-lion and seven billion years ago, when the universe was be-tween one half and two thirds of its present age. Both groupswere hit with a major surprise: the supernovae are fainterthan expected. The difference is slight, the distant supernovaebeing, on average, only 25 percent dimmer than forecast. Butthis result is enough to call long-standing cosmological the-ories into question.

Before drawing any sweeping conclusions, astronomers onboth teams have been asking themselves whether there is a pro-saic explanation for the relative dimness of these distant su-pernovae. One culprit could be murkiness caused by cosmicdust, which might screen out some of the light. We think wecan discount this possibility, however, because dust grainswould tend to filter out blue light more than red, causing thesupernovae to appear redder than they really are (in the sameway that atmospheric dust colors the setting sun). We observeno such alteration. Also, we would expect that cosmic dust, un-less it is spread very smoothly throughout space, would intro-duce a large amount of variation in the measurements, whichwe do not see either.

Another possible disturbance is gravitational lensing, thebending of light rays as they skirt galaxies en route. Such lens-ing occasionally causes brightening, but most often it causesdemagnification and thus can contribute to the dimness of dis-tant supernovae. Yet calculations show that this effect be-comes important only for sources located even farther awaythan the supernovae we are studying, so we can dismiss thiscomplication as well.

Finally, we worried that the distant supernovae are some-how different from the nearby ones, perhaps forming fromyounger stars that contain fewer heavy elements than is typicalin more mature galaxies. Although we cannot rule out this pos-sibility, our analysis already tries to take such differences intoaccount. These adjustments appear to work well when we ap-ply them to nearby galaxies, which range widely in age, make-up and the kinds of supernovae seen.

Because none of these mundane effects fits the new obser-vations, we and many other scientists are now led to think thatthe unexpected faintness of distant supernovae is indeed causedby the structure of the cosmos. Two different properties ofspace and of time might be contributing.

First, space might have negative curvature. Such warping iseasier to comprehend with a two-dimensional analogy. Crea-

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Deceleratingexpansion

SUPERNOVA OBSERVATIONS by the authors’ team (reddots) deviate slightly but significantly from the patternthat many theoreticians expected—namely, a fairly rapid deceleration (blue line) that should occur if theuniverse is “flat” and has no cosmological constant. These observations indicate that the universe has only 20 percent of the matter necessary to make it flat,because it is decelerating more slowly than predicted(black line). The measurements even suggest thatexpansion is accelerating, perhaps because of a nonzerocosmological constant (red line).


tures living in a perfectly flat, two-dimensional world (like thecharacters in Edwin A. Abbott’s classic novel Flatland) wouldfind that a circle of radius r has a circumference of exactly 2πr.But if their world were subtly bent into a saddle shape, it wouldhave a slight negative curvature. The two-dimensional residentsof Saddleland might be oblivious to this curvature until theymeasured a large circle of some set radius and discovered thatits circumference was greater than 2πr.

Most cosmologists have assumed, for various theoreticalreasons, that our three-dimensional space, like Flatland, is notcurved. But if it had negative curvature, the large sphere of ra-diation given off by an ancient supernova would have a greaterarea than it does in geometrically flat space, making the sourceappear strangely faint.

A second explanation for the unexpected dimness of distantsupernovae is that they are farther away than their redshiftssuggest. Viewed another way, supernovae located at theseenormous distances seem to have less redshift than anticipat-ed. To account for the smaller redshift, cosmologists postulatethat the universe must have expanded more slowly in the pastthan they had expected, giving less of an overall stretch to theuniverse and to the light traveling within it.

The ForceWHAT IS THE S IGNIF ICANCE of the cosmic expansionslowing less quickly than previously thought? If the universeis made of normal matter, gravity must steadily slow the ex-

pansion. Little slowing, as indicated by the supernovae mea-surements, thus implies that the overall density of matter in theuniverse is low.

Although this conclusion undermines theoretical preconcep-tions, it agrees with several lines of evidence. For example, as-tronomers have noted that certain stars appear to be older thanthe accepted age of the universe—a clear impossibility. But if thecosmos expanded more slowly in the past, as the supernovae

now indicate, the age of the universe must be revised upward,which may resolve the conundrum. The new results also accordwith other recent attempts to ascertain the total amount of mat-ter, such as studies of galaxy clusters [see “The Evolution ofGalaxy Clusters,” by J. Patrick Henry, Ulrich G. Briel and HansBöhringer; Scientific American, December 1998].

What does the new understanding of the density of matterin the universe say about its curvature? According to the prin-ciples of general relativity, curvature and deceleration are con-nected. To paraphrase John A. Wheeler, formerly at PrincetonUniversity: matter tells spacetime how to curve, and spacetimetells matter how to move. A small density of matter implies neg-ative curvature as well as little slowing. If the universe is nearlyempty, these two dimming effects are both near their theoreti-cal maximum.


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If the cosmos expanded more slowly in the past,as supernovae indicate, the age of the universe

must be revised upward.

DISTANT SUPERNOVA, with a redshift of z = 0.66, appears by the arrow. The explosion of this star affects just a few picture elements in the imagetaken after the event.


The big surprise is that the supernovae we see are fainterthan predicted even for a nearly empty universe (which has max-imum negative curvature). Taken at face value, our observationsappear to require that expansion is actually accelerating withtime. A universe composed only of normal matter cannot growin this fashion, because its gravity is always attractive. Yet ac-cording to Einstein’s theory, the expansion can speed up if anexotic form of energy fills empty space everywhere. This strange“dark energy” is embodied in Einstein’s equations as the so-called cosmological constant. Unlike ordinary forms of massand energy, the dark energy adds gravity that is repulsive andcan drive the universe apart at ever increasing speeds [see “Cos-mological Antigravity,” on page 30]. Once we admit this ex-traordinary possibility, we can explain our observations per-fectly, even assuming the flat geometry beloved by theorists.

Indeed, studies of a completely different kind—sky maps ofthe cosmic background radiation—have recently uncoverednew and compelling evidence for a flat average geometry.Sound waves in the radiation matter plasma of the early uni-verse, whose physical size can be computed from first princi-ples, produce a blotchy pattern of anisotropy on the sky. Theobserved angular size of the pattern shows that the geometryis flat to high precision, implying that the radius of the wholecosmic hypersphere is very much larger than the piece of theuniverse we can observe (much like a small piece of the curved

the earth seems flat). This flat geometry requires a total densi-ty of mass energy much greater than the total estimated densi-ty of normally gravitating matter, providing independent, if in-direct, evidence that most of the stuff of the universe is madeof exotic dark energy. It is striking that a multitude of increas-ingly precise independent techniques converge on a concordantcosmology with this deeply surprising new ingredient.

Evidence for a strange form of energy imparting a repulsivegravitational force is the most interesting result we could havehoped for, yet it is so astonishing that we and others remainsuitably skeptical. Fortunately, advances in the technologyavailable to astronomers, such as new infrared detectors andthe Next Generation Space Telescope, will soon permit us totest our conclusions by offering greater precision and reliabil-ity. These marvelous instruments will also allow us to perceiveeven fainter beacons that flared still longer ago in galaxies thatare much, much farther away.


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The Little Book of the Big Bang. Craig J. Hogan. Springer-Verlag, 1998.

Discovery of a Supernova Explosion at Half the Age of the Universe. S. Perlmutter, G. Aldering, M. Della Valle, S. Deustua, R. S. Ellis, S. Fabbro, A. Fruchter, G. Goldhaber, D. E. Groom, I. M. Hook, A. G. Kim, M. Y. Kim, R. A. Knop, C. Lidman, R. G. McMahon, Peter Nugent, R. Pain, N. Panagia, C. R. Pennypacker, P. Ruiz-Lapuente, B. Schaefer and N. Walton (TheSupernova Cosmology Project) in Nature, Vol. 391, pages 51–54; January1, 1998. Preprint available at xxx.lanl.gov/abs/astro-ph/9712212

Observational Evidence from Supernovae for an Accelerating Universeand a Cosmological Constant. Adam G. Riess, Alexei V. Filippenko, PeterChallis, Alejandro Clocchiattia, Alan Diercks, Peter M. Garnavich, Ron L.Gilliland, Craig J. Hogan, Saurabh Jha, Robert P. Kirshner, B. Leibundgut,M. M. Phillips, David Reiss, Brian P. Schmidt, Robert A. Schommer, R. ChrisSmith, J. Spyromilio, Christopher Stubbs, Nicholas B. Suntzeff and JohnTonry in Astronomical Journal, Vol. 116, No. 3, pages 1009–1038;September 1998. Preprint at xxx.lanl.gov/abs/astro-ph/9805201

Additional information on supernova searches is available at cfa-www.harvard.edu/cfa/oir/Research/supernova/HighZ.html and www.supernova.lbl.gov/


IN APRIL 2001 NASA’s Hubble Space Telescope captured the mostdistant supernova ever seen (above and below, right), whicherupted 10 billion years ago. By examining its glow (below, left),cosmologists have found more convincing evidence thatrepulsive, dark energy is accelerating the universe’s expansion.


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THE LONG-DERIDED

COSMOLOGICAL

CONSTANT—

A CONTRIVANCE OF

ALBERT EINSTEIN’S—

MAY EXPLAIN CHANGES

IN THE EXPANSION RATE

OF THE UNIVERSE

ANTIGRAVITYBY LAWRENCE M. KRAUSS

Cosmological

SO-CALLED EMPTY SPACE is actually filled with elementary particles thatpop in and out of existence too quickly to be detected directly. Theirpresence is the consequence of a basic principle of quantum mechanicscombined with special relativity: nothing is exact, not even nothingness.The aggregate energy represented by these virtual particles, like otherforms of energy, could exert a gravitational force, which could be eitherattractive or repulsive depending on physical principles that are not yetunderstood. On macroscopic scales the energy could act as thecosmological constant proposed by Albert Einstein.

U p d a t e d f r o m t h e J a n u a r y 1 9 9 9 i s s u e 31COPYRIGHT 2002 SCIENTIFIC AMERICAN, INC.


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“To see what is in front of one’s nose requires a constant strug-gle.” These words aptly describe the workings of modern cos-mology. The universe is all around us—we are part of it—yetscientists must sometimes look halfway across it to understandthe processes that led to our existence on the earth. And al-though researchers believe that the underlying principles of na-ture are simple, unraveling them is another matter. The cluesin the sky can be subtle. Orwell’s adage is doubly true for cos-mologists grappling with the recent observations of explodingstars hundreds of millions of light-years away. Contrary tomost expectations, they are finding that the expansion of theuniverse may not be slowing down but rather speeding up.

Astronomers have known that the visible universe is ex-panding since at least 1929, when Edwin P. Hubble demon-strated that distant galaxies are moving apart as they would ifthe entire cosmos were uniformly swelling in size. These out-ward motions are counteracted by the collective gravity ofgalaxy clusters and all the planets, stars, gas and dust they con-tain. Even the minuscule gravitational pull of, say, a paper clipretards cosmic expansion by a slight amount. A decade ago acongruence of theory and observations suggested that therewere enough paper clips and other matter in the universe toalmost, but never quite, halt the expansion. In the geometricterms that Albert Einstein encouraged cosmologists to adopt,the universe seemed to be “flat.”

The flat universe is an intermediate between two other plau-sible geometries, called “open” and “closed.” In a cosmos wherematter does battle with the outward impulse from the big bang,the open case represents the victory of expansion: the universewould go on expanding forever. In the closed case, gravitywould have the upper hand, and the universe would eventual-ly collapse again, ending in a fiery “big crunch.” The open, closedand flat scenarios are analogous to launching a rocket fasterthan, slower than or exactly at the earth’s escape velocity—thespeed necessary to overcome the planet’s gravitational attraction.

That we live in a flat universe, the perfect balance of pow-er, is one of the hallmark predictions of standard inflationarytheory, which postulates a very early period of rapid expansionto reconcile several paradoxes in the conventional formulationof the big bang. Although the visible contents of the cosmos areclearly not enough to make the universe flat, celestial dynamicsindicate that there is far more matter than meets the eye. Mostof the material in galaxies and assemblages of galaxies must beinvisible to telescopes. Over a decade ago I applied the term“quintessence” to this so-called dark matter, borrowing a termAristotle used for the ether—the invisible material supposed to

permeate all of space [see “Dark Matter in the Universe,” byLawrence M. Krauss; Scientific American, December 1986].

Yet an overwhelming body of evidence now implies thateven the unseen matter is not enough to produce a flat universe.If that is so, its main constituents cannot be visible matter, darkmatter or radiation. Instead the universe must be composedlargely of an even more ethereal form of energy that inhabitsempty space, including that which is in front of our noses.

Fatal AttractionThe idea of such energy has a long and checkered history,which began when Einstein completed his general theory of rel-ativity, more than a decade before Hubble’s convincing demon-stration that the universe is expanding. By tying together space,time and matter, relativity promised what had previously beenimpossible: a scientific understanding not merely of the dy-namics of objects within the universe but of the universe itself.There was only one problem. Unlike other fundamental forcesfelt by matter, gravity is universally attractive—it only pulls; itcannot push. The unrelenting gravitational attraction of mat-ter could cause the universe to collapse eventually. So Einstein,who presumed the universe to be static and stable, added anextra term to his equations, a “cosmological term,” whichcould stabilize the universe by producing a new long-rangeforce throughout space. If its value were positive, the termwould represent a repulsive force—a kind of antigravity thatcould hold the universe up under its own weight.

Alas, within five years Einstein abandoned this kludge,which he associated with his “biggest blunder.” The stabilityoffered by the term turned out to be illusory, and, more im-portant, evidence had begun to mount that the universe is ex-panding. As early as 1923, Einstein wrote in a letter to mathe-matician Hermann Weyl that “if there is no quasi-static world,then away with the cosmological term!” Like the ether beforeit, the term appeared to be headed for the dustbin of history.

Physicists were happy to do without such an intrusion. In

LAWRENCE M. KRAUSS works at the interface of physics and as-tronomy. He studies the workings of stars, black holes, gravita-tional lenses and the early universe in order to shed light on par-ticle physics beyond the current Standard Model, including theunification of forces, quantum gravity and explanations for darkmatter. Krauss is currently chair of the physics department atCase Western Reserve University. He is the author of six books,most recently Atom: A Single Oxygen Atom’s Odyssey from the BigBang to Life on Earth . . . and Beyond (Back Bay Books, 2002).

THE

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Novelist and social critic George Orwell wrote in 1946,


the general theory of relativity, the source of gravitationalforces (whether attractive or repulsive) is energy. Matter is sim-ply one form of energy. But Einstein’s cosmological term is dis-tinct. The energy associated with it does not depend on posi-tion or time—hence the name “cosmological constant.” Theforce caused by the constant operates even in the complete ab-sence of matter or radiation. Therefore, its source must be a cu-rious energy that resides in empty space. The cosmological con-stant, like the ether, endows the void with an almost metaphys-ical aura. With its demise, nature was once again reasonable.

Or was it? In the 1930s glimmers of the cosmological con-stant arose in a completely independent context: the effort tocombine the laws of quantum mechanics with Einstein’s spe-cial theory of relativity. Physicists Paul A. M. Dirac and laterRichard Feynman, Julian S. Schwinger and Shinichiro Tomo-naga showed that empty space was more complicated thananyone had previously imagined. Elementary particles, itturned out, can spontaneously pop out of nothingness and dis-appear again, if they do so for a time so short that one cannotmeasure them directly [see “Exploiting Zero-Point Energy,” byPhilip Yam; Scientific American, December 1997]. Such vir-tual particles, as they are called, may appear as far-fetched asangels sitting on the head of a pin. But there is a difference. Theunseen particles produce measurable effects, such as alterationsto the energy levels of atoms as well as forces between nearbymetal plates. The theory of virtual particles agrees with obser-vations to nine decimal places. (Angels, in contrast, normallyhave no discernible effect on either atoms or plates.) Like it ornot, empty space is not empty after all.

Virtual RealityIF VIRTUAL PARTICLES can change the properties of atoms,might they also affect the expansion of the universe? In 1967

Russian astrophysicist Yakov B. Zeldovich showed that the en-ergy of virtual particles should act precisely as the energy as-sociated with a cosmological constant. But there was a seriousproblem. Quantum theory predicts a whole spectrum of vir-tual particles, spanning every possible wavelength. Whenphysicists add up all the effects, the total energy comes out in-finite. Even if theorists ignore quantum effects smaller than acertain wavelength—for which poorly understood quantumgravitational effects presumably alter things—the calculatedvacuum energy is roughly 120 orders of magnitude larger thanthe energy contained in all the matter in the universe.

What would be the effect of such a humongous cosmolog-ical constant? Taking a cue from Orwell’s maxim, you can eas-ily put an observational limit on its value. Hold out your handand look at your fingers. If the constant were as large as quan-tum theory naively suggests, the space between your eyes andyour hand would expand so rapidly that the light from yourhand would never reach your eyes. To see what is in front ofyour face would be a constant struggle (so to speak), and youwould always lose. The fact that you can see anything at allmeans that the energy of empty space cannot be large. And thefact that we can see not only to the ends of our arms but alsoto the far reaches of the universe puts an even more stringentlimit on the cosmological constant: almost 120 orders of mag-nitude smaller than the estimate mentioned above. The dis-crepancy between theory and observation is the most perplex-ing quantitative puzzle in physics [see “The Mystery of the Cos-mological Constant,” by Larry Abbott; Scientific American,May 1988].

The simplest conclusion is that some as yet undiscoveredphysical law causes the cosmological constant to vanish. But asmuch as theorists might like the constant to go away, variousastronomical observations—of the age of the universe, the den-


VISIBLE MATTER

BARYONIC DARK MATTER

NONBARYONIC DARK MATTER

COSMOLOGICALDARK ENERGY

Ordinary matter (composed mainly of protons and

neutrons) that forms stars, dust and gas

Ordinary matter that is too dim to see, perhaps

brown or black dwarfs (massive compact halo

objects, or MACHOs)

Exotic particles such as “axions,” neutrinos with

mass or weakly interacting massive particles (WIMPs)

Cosmological constant

(energy of empty space)

Telescope observations

Big bang nucleosynthesis calculations

and observed deuterium abundance

Gravity of visible matter is insufficient to

account for orbital speeds of stars within

galaxies and of galaxies within clusters

Microwave background suggests cosmos

is flat, but there is not enough baryonic

or nonbaryonic matter to make it so

0.01

0.05

0.3

0.7

APPROXIMATE TYPE LIKELY COMPOSITION MAIN EVIDENCE CONTRIBUTION TO Ω

CONTENTS OF THE UNIVERSE include billions of galaxies, each one containing an equally mind-boggling number of stars. Yet the bulk of matter seems to

consist of dark matter, whose identity is still uncertain. The cosmological constant, if its existence is confirmed, would act like a yet more exotic form of

dark energy on cosmological scales. The quantity omega (Ω) is the ratio of the density of matter or energy to the density required for flatness. —L.M.K.

Types of Matter


sity of matter and the nature of cosmic structures—all inde-pendently suggest that it may be here to stay.

Determining the age of the universe is one of the long-stand-ing issues of modern cosmology. By measuring the velocities ofgalaxies, astronomers can calculate how long it took them toarrive at their present positions, assuming they all started outat the same place. For a first approximation, one can ignore thedeceleration caused by gravity. Then the universe would ex-

pand at a constant speed and the time interval would just bethe ratio of the distance between galaxies to their measuredspeed of separation—that is, the reciprocal of the famous Hub-ble constant. The higher the value of the Hubble constant, thefaster the expansion rate and hence the younger the universe.

Hubble’s first estimate of his eponymous constant was al-most 500 kilometers per second per megaparsec—whichwould mean that two galaxies separated by a distance of onemegaparsec (about three million light-years) are moving apart,on average, at 500 kilometers per second. This value wouldimply a cosmic age of about two billion years, which is inpainful contradiction with the known age of the earth—aboutfour billion years. When the gravitational attraction of matteris taken into account, the analysis predicts that objects movedfaster early on, taking even less time to get to their present po-sitions than if their speed had been constant. This refinementreduces the age estimate by one third, unfortunately worsen-ing the discrepancy.

Over the past seven decades, astronomers have improvedtheir determination of the expansion rate, but the tension be-

tween the calculated age of the universe and the age of objectswithin it has persisted. In the past decade, with the launch ofthe Hubble Space Telescope and the development of new ob-servational techniques, disparate measurements of the Hub-ble constant are finally beginning to converge. Wendy L. Freed-man of the Carnegie Observatories and her colleagues have in-ferred a value of 73 kilometers per second per megaparsec (witha most likely range, depending on experimental error, of 65 to

81). These results put the upper limit on the age of a flat uni-verse at about 10 billion years.

The Age CrisisI S THAT VALUE OLD ENOUGH? It depends on the age ofthe oldest objects that astronomers can date. Among the mostancient stars in our galaxy are those found in tight groupsknown as globular clusters, some of which are located in theoutskirts of our galaxy and are thus thought to have formedbefore the rest of the Milky Way. Estimates of their age, basedon calculations of how fast stars burn their nuclear fuel, tradi-tionally ranged from 15 billion to 20 billion years. Such objectsappeared to be older than the universe.

To determine whether this age conflict was the fault of cos-mology or of stellar modeling, in 1995 my colleagues—Brian C.Chaboyer, then at the Canadian Institute of Theoretical Astro-physics, Pierre Demarque of Yale University and Peter J. Ker-nan of Case Western Reserve University—and I reassessed theglobular cluster ages. We simulated the life cycles of three mil-lion different stars whose properties spanned the existing un-


DEMONSTRATION OF CASIMIR EFFECT is oneway that physicists have corroborated the

theory that space is filled with fleeting virtual particles. The Casimir effect

generates forces between metal objects—forinstance, an attractive force between

parallel metal plates (near right). Looselyspeaking, the finite spacing of the plates

prevents virtual particles larger than acertain wavelength from materializing in the

gap. Therefore, there are more particlesoutside the plates than between them, an

imbalance that pushes the plates together( far right). The Casimir effect has a

distinctive dependence on the shape of theplates, which allows physicists to tease it out

from other forces of nature. —L.M.K.Casimir plates

Vacuumfluctuations

The cosmological constant provides much of the force that holds the universe up

under its own weight.

PARTICLES IN EMPTY SPACE

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MAP OF MODELS shows how the unfolding of the universe depends on twokey cosmological quantities: the average density of matter (horizontalaxis) and the density of energy in the cosmological constant (vertical axis).Their values, given here in standard cosmological units, have three distincteffects. First, their sum (which represents the total cosmic energy content)determines the geometry of spacetime (yellow line). Second, their difference

(which represents the relative strength of expansion and gravity) determineshow the expansion rate changes over time (blue line). These two effects havebeen probed by recent observations (shaded regions). The third, a balance ofthe two densities, determines the fate of the universe (red line). The threeeffects have many permutations—unlike the view in which the cosmologicalconstant is assumed to be zero and there are only two possible outcomes.

ACCELERATING

(cosmological constant overpowers matter)

CONSTANTEXPANSION

NO BIG BANG

(density

of matte

r could never

have been infin

ite)

DECELERATING

(matter overpowers cosmological constant)

STEADY EXPANSION(matter cannot stop

outward impulse)

ASYMPTOTE TO EINSTEIN’S ORIGINAL

STATIC MODEL

OLD STANDARDMODEL

NEW PREFERRED MODEL(consistent with all data)

RANGE OF SUPERNOVA DATA

1

0

–10 1 2 3

3

2

RANGE OFMICROWAVE

BACKGROUND DATA

RANGE OFCLUSTER

DATA

RULED OUT BY AGE

(universe would be

younger than oldest s

tars)

RECOLLAPSE(universe expands and

contracts at least once)

CLOSED

(total energy density exceeds value

required for flatness)

OPEN

(total energy density is less than

value required for flatness)

FLAT

Ω MATTER

ΩCO

SMOL

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AL C

ONST

ANT


certainties and then compared our model stars with those inglobular clusters. The oldest, we concluded, could be as youngas 12.5 billion years old, which was still at odds with the age ofa flat, matter-dominated universe.

But two years ago the Hipparcos satellite, launched by theEuropean Space Agency to measure the locations of more than100,000 nearby stars, revised the distances to these stars and,indirectly, to globular clusters. The new distances affected es-timates of their brightness and forced us to redo our analysis,because brightness determines the rate at which stars consumefuel and hence their life spans. Although the newly derived ageswere somewhat smaller, the most recent analysis by our groupputs a best-fit age of the universe at 13.4 billion years, with alower limit of 11.2 billion years, clearly in conflict with the up-per limit for a flat, matter-dominated universe.

A lower density of matter, signifying an open universe withslower deceleration, would ease the tension somewhat. Evenso, the only way to lift the age above 12.5 billion years wouldbe to consider a universe dominated not by matter but by a cos-mological constant. The resulting repulsive force would causethe Hubble expansion to accelerate over time. Galaxies wouldhave been moving apart slower than they are today, taking

longer to reach their present separation, so the universe wouldbe older.

Meanwhile other pillars of observational cosmology haverecently been shaken, too. As astronomers have used the lat-est technology to survey ever larger regions of the cosmos, theirability to tally up its contents has improved. Now the case iscompelling that the total amount of matter is insufficient toyield a flat universe.

This cosmic census first involves calculations of the syn-thesis of elements by the big bang. The light elements in the cos-mos—hydrogen and helium and their rarer isotopes, such asdeuterium—were created in the early universe in relativeamounts that depended on the number of available protonsand neutrons, the constituents of normal matter. Thus, by com-paring the abundances of the various isotopes, astronomers candeduce the total amount of ordinary matter that was producedin the big bang. (There could, of course, also be other matternot composed of protons and neutrons.)

The relevant observations took a big step forward in 1996,when David R. Tytler and Scott Burles of the University of Cal-ifornia at San Diego and their colleagues measured the pri-mordial abundance of deuterium using absorption of quasar

light by intergalactic hydrogen clouds. Be-cause these clouds have never contained stars,their deuterium could have been created onlyby the big bang. Tytler and Burles’s findingimplies that the average density of ordinarymatter is between 4 and 7 percent of theamount needed for the universe to be flat.

Astronomers have also probed the densi-ty of matter by studying the largest gravita-tionally bound objects in the universe: clustersof galaxies. These groupings of hundreds ofgalaxies account for almost all visible matter.Most of their luminous content takes the formof hot intergalactic gas, which emits x-rays.The temperature of this gas, inferred from thespectrum of the x-rays, depends on the totalmass of the cluster: in more massive clusters,the gravity is stronger and hence the pressurethat supports the gas against gravity must belarger, which drives the temperature higher.In 1993 Simon D. M. White, now at the MaxPlanck Institute for Astrophysics in Garching,Germany, and his colleagues compiled infor-mation about several different clusters to ar-gue that luminous matter accounted for be-tween 10 and 20 percent of the total mass ofthe objects. When combined with the mea-surements of deuterium, these results implythat the total density of clustered matter—in-cluding protons and neutrons as well as moreexotic particles such as certain dark mattercandidates—is at most 60 percent of that re-quired to flatten the universe. G

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10–20

10–21

10–22

10–23

10–24

10–25

10–26

10–27

10–28

10–29

10–30

10–31

0 5 10 15 20First galaxiesformed

Solarsystemformed

Now Oursundies

Dens

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gram

s pe

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Age (billions of years)


Matter

COSMIC COINCIDENCE is one of many mysteries swirling about the cosmological constant.The average density of ordinary matter decreases as the universe expands (red). Theequivalent density represented by the cosmological constant is fixed (black). So why,despite these opposite behaviors, do the two have nearly the same value today? The con-sonance is either happenstance, a precondition for human existence (an appeal to the weakanthropic principle) or an indication of a mechanism not currently envisaged. —L.M.K.


AVERAGE DENSITY OF THE UNIVERSE


A third set of observations, ones that also bear on the dis-tribution of matter at the largest scales, supports the view thatthe universe has too little mass to make it flat. Perhaps no oth-er subfield of cosmology has advanced so much in the past 20years as the understanding of the origin and nature of cosmicstructures. Astronomers had long assumed that galaxies coa-lesced from slight concentrations of matter in the early uni-verse, but no one knew what would have produced such un-dulations. The development of the inflationary theory in the1980s provided the first plausible mechanism—namely, the en-largement of quantum fluctuations to macroscopic size.

Numerical simulations of the growth of structures follow-ing inflation have shown that if dark matter was not made fromprotons and neutrons but from some other type of particle(such as so-called WIMPs), tiny ripples in the cosmic micro-wave background radiation could grow into the structures nowseen. Moreover, concentrations of matter should still be evolv-ing into clusters of galaxies if the overall density of matter is

high. The relatively slow growth of the number of rich clus-ters over the recent history of the universe suggests that the den-sity of matter is less than 50 percent of that required for a flatuniverse [see “The Evolution of Galaxy Clusters,” by J. PatrickHenry, Ulrich G. Briel and Hans Böhringer; Scientific Amer-ican, December 1998].

Nothing MattersTHESE MANY FINDINGS that the universe has too little mat-ter to make it flat have become convincing enough to overcomethe strong theoretical prejudice against this possibility. Two in-terpretations are possible: either the universe is open, or it ismade flat by some additional form of energy that is not associ-ated with ordinary matter. To distinguish between these alter-natives, astronomers have been pushing to measure the micro-wave background at high resolution. The cosmic microwavebackground—the literal afterglow of the big bang—emanatesfrom a “last scattering” surface located more than 12 billionlight-years away from us. The surface represents a time whenthe universe first cooled sufficiently so that the previously ion-ized plasma of protons and electrons could combine to formneutral hydrogen, which is transparent to radiation.

When we measure the CMB radiation today in different di-rections, we are measuring regions that were far enough apartthat they could not have been in casual contact back then. Re-gions separated by less than about a degree could have beentraversed at the speed of light over the 300,000 years or so ittook the radiation gas to cool. This angular scale should leavea remnant imprint in the CMB “map” that current detectorsmeasure. The actual angular scale associated with this distance,however, depends on the geometry of the universe. In a flat uni-verse, light rays travel in straight lines as one traces them backto their source. In an open universe, light rays diverge as onetraces them back, and in a closed universe they converge. Inan open universe, therefore, the characteristic angular scale as-sociated with this “horizon size” at the last scattering surfaceshould be smaller than it would appear if the universe were flat,and in a closed universe it should be larger. Since late 1998 theBOOMERanG (Balloon Observations of Millimetric Extra-galactic Radiation and Geophysics) experiment in Antarctica,as well as other balloon experiments in Canada and the U.S.,has found definitive evidence of this angular signature’s exis-tence. Moreover, the fact that it corresponds to an angular scaleof about one degree provides, for the very first time, a directmeasurement of the geometry of the universe. And the universedoes appear to be precisely flat.

Meanwhile researchers studying distant supernovae haveprovided the first direct, if tentative, evidence that the expan-sion of the universe is accelerating, a telltale sign of a cosmo-logical constant with the same value implied by the other data[see “Surveying Spacetime with Supernovae,” on page 22]. Ob-servations of the microwave background and of supernovae il-luminate two different aspects of cosmology. The microwavebackground reveals the geometry of the universe, which is sen-sitive to the total density of energy, in whatever form, where-


The Fate of the UniverseTHE COSMOLOGICAL CONSTANT changes the usual simplepicture of the future of the universe. Traditionally, cosmologyhas predicted two possible outcomes that depend on thegeometry of the universe or, equivalently, on the averagedensity of matter. If the density of a matter-filled universeexceeds a certain critical value, it is “closed,” in which case it willeventually stop expanding, start contracting and ultimatelyvanish in a fiery apocalypse. If the density is less than thecritical value, the universe is “open” and will expand forever. A“flat” universe, for which the density equals the critical value,also will expand forever but at an ever slower rate.

Yet these scenarios assume that the cosmological constantequals zero. If not, it—rather than matter—may control theultimate fate of the universe. The reason is that the constant, bydefinition, represents a fixed density of energy in space. Mattercannot compete: a doubling in radius dilutes its densityeightfold. In an expanding universe the energy densityassociated with a cosmological constant must win out. If theconstant has a positive value, it generates a long-rangerepulsive force in space, and the universe will continue toexpand even if the total energy density in matter and in spaceexceeds the critical value. (Large negative values of theconstant are ruled out because the resulting attractive forcewould already have brought the universe to an end.)

Even this new prediction for eternal expansion assumes thatthe constant is indeed constant, as general relativity suggeststhat it should be. If in fact the energy density of empty spacedoes vary with time, the fate of the universe will depend on howit does so. And there may be a precedent for such changes—

namely, the inflationary expansion in the primordial universe.Perhaps the universe is just now entering a new era of inflation,one that may eventually come to an end. —L.M.K.


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THREE GEOMETRIES are shown here from two different perspectives: a hypotheticaloutside view that ignores, for the sake of illustration, one of the spatial dimensions (left column) and an inside view that shows all three dimensions as well as a referenceframework (right column). The outside view is useful for seeing the basic geometricrules. The inside view reveals the apparent sizes of objects (which, in these diagrams,are the same actual size) at different distances. Here objects and framework redden with distance.

Flat space obeys the familiar rules of Euclidean geometry. The angular size of identicalspheres is inversely proportional to distance—the usual vanishing-point perspectivetaught in art class.

Spherical space has the geometric properties of a globe. With increasing distance, thespheres at first seem smaller. They reach a minimum apparent size and subsequentlylook larger. (Similarly, lines of longitude emanating from a pole separate, reach amaximum separation at the equator and then refocus onto the opposite pole.) Thisframework consists of dodecahedra.

Hyperbolic space has the geometry of a saddle. Angular size shrinks much more rapidlywith distance than in Euclidean space. Because angles are more acute, five cubelikeobjects fit around each edge, rather than only four.

IF THE UNIVERSE had an “outside” and people couldview it from that perspective, cosmology would bemuch easier. Lacking these gifts, astronomersmust infer the basic shape of the universe from itsgeometric properties. Everyday experienceindicates that space is Euclidean, or “flat,” on smallscales. Parallel lines never meet, triangles span180 degrees, the circumference of a circle is 2πr,and so on. But it would be wrong to assume that theuniverse is Euclidean on large scales, just as itwould be wrong to conclude that the earth is flatjust because a small patch of it looks flat.

There are two other possible three-dimensionalgeometries consistent with the observations ofcosmic homogeneity (the equivalence of all pointsin space) and isotropy (the equivalence of alldirections). They are the spherical, or “closed,”geometry and the hyperbolic, or “open,” geometry.Both are characterized by a curvature lengthanalogous to the earth’s radius. If the curvature ispositive, the geometry is spherical; if negative,hyperbolic. For distances much smaller than thislength, all geometries look Euclidean.

In a spherical universe, as on the earth’ssurface, parallel lines eventually meet, trianglescan span up to 540 degrees, and the circumferenceof a circle is smaller than 2πr. Because the spacecurves back on itself, the spherical universe isfinite. In a hyperbolic universe, parallel linesdiverge, triangles have less than 180 degrees,and the circumference of a circle is larger than2πr. Such a universe, like Euclidean space, isinfinite in size.

These three geometries have quite differenteffects on perspective (see illustration at right),which distort the appearance of features in thecosmic microwave background radiation. Thelargest ripples in the background have the sameabsolute size regardless of the process of infla-tion. If the universe is flat, the largest undulationswould appear to be about one degree across. But ifthe universe is hyperbolic, the same featuresshould appear to be only half that size, simplybecause of the geometric distortion of light rays.

Ground and balloon-borne observationssuggest that the ripples are one degree across,which implies that the universe is nearly flat. The Microwave Anisotropy Probe, which isexpected to return data soon, will make definitivemeasurements of these fluctations.

THE GEOMETRY OF THE UNIVERSE

Martin A. Bucher and David N. Spergel study the physics of the very earlyuniverse. Bucher is professor of applied mathematics and theoretical physicsat the University of Cambridge. Spergel is professor of astrophysical sciencesat Princeton University.

By Martin A. Bucher and David N. Spergel


as the supernovae directly probe the expansion rate of the uni-verse, which depends on the difference between the density ofmatter (which slows the expansion) and the cosmological con-stant (which can speed it up).

Together all these results suggest that the constant con-tributes between 50 and 75 percent of the energy needed tomake the universe flat [see illustration on page 35]. Despite thepreponderance of evidence, it is worth remembering the oldsaw that an astronomical theory whose predictions agree withall observations is probably wrong, if only because some of themeasurements or some of the predictions are likely to be erro-neous. Nevertheless, theorists are already scrambling to un-derstand what 20 years ago would have been unthinkable: acosmological constant greater than zero yet much smaller thancurrent quantum theories predict. Some feat of fine-tuning mustsubtract virtual-particle energies to 123 decimal places butleave the 124th untouched—a precision seen nowhere else innature.

One direction, explored by Steven Weinberg of the Uni-versity of Texas at Austin and his colleagues, invokes the lastresort of cosmologists, the anthropic principle. If the observeduniverse is merely one of an infinity of disconnected univers-es—each of which might have slightly different constants of na-ture, as suggested by some incarnations of inflationary theorycombined with emerging ideas of quantum gravity—thenphysicists can hope to estimate the magnitude of the cosmo-logical constant by asking in which universes intelligent life islikely to evolve. Weinberg and others have arrived at a resultthat is compatible with the apparent magnitude of the cosmo-logical constant.

Most theorists, however, do not find these notions con-vincing, as they imply that there is no reason for the constantto take on a particular value; it just does. Although that argu-ment may be true, physicists have not yet exhausted the otherpossibilities, which might allow the constant to be constrainedby fundamental theory rather than by accidents of history.

Another direction of research follows in a tradition estab-lished by Dirac. He argued that there is one measured largenumber in the universe—its age (or, equivalently, its size). If cer-tain physical quantities were changing over time, they mightnaturally be either very large or very small today [see “P.A.M.Dirac and the Beauty of Physics,” by R. Corby Hovis and HelgeKragh; Scientific American, May 1993]. The cosmologicalconstant could be one example. It might not, in fact, be con-stant. After all, if the cosmological constant is fixed and nonze-ro, we are living at the first and only time in the cosmic histo-ry when the density of matter, which decreases as the universeexpands, is comparable to the energy stored in empty space.Why the coincidence? Several groups have instead imaginedthat some form of cosmic energy mimics a cosmological con-stant but varies with time.

This concept was explored by P. James E. Peebles andBharat V. Ratra of Princeton University more than a decadeago. Motivated by the new supernova findings, other groupshave resurrected the idea. Some have drawn on emerging con-

cepts from string theory. Robert R. Caldwell of DartmouthCollege and Paul J. Steinhardt of Princeton have reproposedthe term “quintessence” to describe this variable energy [see“The Quintessential Universe,” on page 40]. It is one measureof the theoretical conundrum that the dark matter that origi-nally deserved this term now seems almost mundane by com-parison. As much as I like the word, none of the theoreticalideas for quintessence seems compelling. Each is ad hoc. Theenormity of the cosmological-constant problem remains.

How will cosmologists know for certain whether they haveto reconcile themselves to this theoretically perplexing universe?New measurements of the microwave background and ofgalaxy evolution, the continued analysis of distant supernovaeand measurements of gravitational lensing of distant quasarsshould be able to pin down the cosmological constant over thenext few years. One thing is already certain. The standard cos-mology of the 1980s, postulating a flat universe dominated bymatter, is dead. The universe appears to be filled with an ener-gy of unknown origin. This will require a dramatic new under-standing of physics. Put another way, “nothing” could not pos-sibly be more interesting.


Dreams of a Final Theory. Steven Weinberg. Pantheon Books, 1992.

Principles of Physical Cosmology. P. James E. Peebles. Princeton University Press, 1993.

Before the Beginning: Our Universe and Others. Martin Rees. Addison-Wesley, 1997.

The Age of Globular Clusters in Light of Hipparcos: Resolving the AgeProblem? Brian Chaboyer, Pierre Demarque, Peter J. Kernan andLawrence M. Krauss in Astrophysical Journal, Vol. 494, No. 1, pages 96–110; February 10, 1998. Preprint available atxxx.lanl.gov/abs/astro-ph/9706128

The End of the Age Problem, and the Case for a Cosmological ConstantRevisited. Lawrence M. Krauss in Astrophysical Journal, Vol. 501, No. 2,pages 461–466; July 10, 1998. Preprint available atxxx.lanl.gov/abs/astro-ph/9706227

Living with Lambda. J. D. Cohn. Preprint available atxxx.lanl.gov/abs/astro-ph/9807128

Quintessence. Lawrence M. Krauss. Basic Books, 2001.


OBSERVATION ΩMATTER

Age of universe <1

Density of protons and neutrons 0.3–0.6

Galaxy clustering 0.3–0.4

Galaxy evolution 0.3–0.5

Cosmic microwave background radiation <~1

Supernovae type Ia 0.2–0.5

Summary of Inferred Values of Cosmic Matter DensityMEASUREMENTS of the contribution to Ω from matter are in rough

concordance. Most astronomers now accept that matter alone cannot

make Ω equal to 1. But other forms of energy, such as the cosmological

constant, may also pitch in. —L.M.K.


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quintessentialUNIVERSE

BY JEREMIAH P. OSTRIKER AND PAUL J. STEINHARDT

The universe has recently beencommandeered by an invisibleenergy field,which is causing itsexpansion to accelerate outward

the


Is it all over but the shouting?Is the cosmos understood aside from mi-nor details? A few years ago it certainlyseemed that way. After a century of vig-orous debate, scientists had reached abroad consensus about the basic historyof the universe. It all began with gas andradiation of unimaginably high tempera-ture and density. For 15 billion years, ithas been expanding and cooling. Galax-ies and other complex structures havegrown from microscopic seeds—quantumfluctuations—that were stretched to cos-mic size by a brief period of “inflation.”We had also learned that only a smallfraction of matter is composed of the nor-mal chemical elements of our everydayexperience. The majority consists of so-called dark matter, primarily exotic ele-

mentary particles that do not interact withlight. Plenty of mysteries remained, but atleast we had sorted out the big picture.

Or so we thought. It turns out that wehave been missing most of the story. Overthe past five years or so, observations haveconvinced cosmologists that the chemicalelements and the dark matter, combined,amount to less than half the content ofthe universe. The bulk is a ubiquitousdark energy with a strange and remark-able feature: its gravity does not attract.It repels. Whereas gravity pulls the chem-ical elements and dark matter into starsand galaxies, it pushes the dark energyinto a nearly uniform haze that permeatesspace. The universe is a battleground be-tween the two tendencies, and repulsivegravity is winning. It is gradually over-whelming the attractive force of ordinary

matter—causing the universe to acceler-ate to ever larger rates of expansion, per-haps leading to a new runaway inflation-ary phase and a totally different future forthe universe than most cosmologists en-visioned a decade ago.

Until recently, cosmologists have fo-cused simply on proving the existence ofdark energy. Having made a convincingcase, they are now turning their attentionto a deeper problem: Where does the en-ergy come from? The best-known possi-bility is that the energy is inherent in thefabric of space. Even if a volume of spacewere utterly empty—without a bit of mat-ter and radiation—it would still containthis energy. Such energy is a venerablenotion that dates back to Albert Einstein

and his attempt in 1917 to construct astatic model of the universe. Like manyleading scientists over the centuries, in-cluding Isaac Newton, Einstein believedthat the universe is unchanging, neithercontracting nor expanding. To coax stag-nation from his general theory of relativ-ity, he had to introduce vacuum energy,or, in his terminology, a cosmologicalconstant. He adjusted the value of theconstant so that its gravitational repul-sion would exactly counterbalance thegravitational attraction of matter.

Later, when astronomers establishedthat the universe is expanding, Einsteinregretted his delicately tuned artifice, call-ing it his greatest blunder. But perhaps hisjudgment was too hasty. If the cosmo-logical constant had a slightly larger val-ue than Einstein proposed, its repulsion

would exceed the attraction of matter,and cosmic expansion would accelerate.

Many cosmologists, though, are nowleaning toward a different idea, known asquintessence. The translation is “fifth el-ement,” an allusion to ancient Greek phi-losophy, which suggested that the uni-verse is composed of earth, air, fire andwater, plus an ephemeral substance thatprevents the moon and planets fromfalling to the center of the celestial sphere.Four years ago Robert R. Caldwell,Rahul Dave and one of us (Steinhardt),all then at the University of Pennsylvania,reintroduced the term to refer to a dy-namical quantum field, not unlike anelectrical or magnetic field, that gravita-tionally repels.

The dynamism is what cosmologistsfind so appealing about quintessence. Thebiggest challenge for any theory of darkenergy is to explain the inferred amountof the stuff—not so much that it wouldhave interfered with the formation ofstars and galaxies in the early universebut just enough that its effect can now befelt. Vacuum energy is completely inert,maintaining the same density for all time.Consequently, to explain the amount ofdark energy today, the value of the cos-mological constant would have to be fine-tuned at the creation of the universe tohave the proper value—which makes itsound rather like a fudge factor. In con-trast, quintessence interacts with matterand evolves with time, so it might natu-rally adjust itself to reach the observedvalue today. JA

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Dark energy differs from dark matter in one major respect: it must be gravitationally repulsive.


Two Thirds of RealityDISTINGUISHING between these twooptions is critically important for physics.Particle physicists have depended onhigh-energy accelerators to discover newforms of energy and matter. Now the cos-mos has revealed an unanticipated typeof energy, too thinly spread and tooweakly interacting for accelerators toprobe. Determining whether the energy isinert or dynamical may be crucial to for-mulating a fundamental theory of nature.Particle physicists are discovering thatthey must keep a close eye on develop-ments in the heavens as well as those inthe accelerator laboratory.

The case for dark energy has beenbuilding brick by brick for nearly adecade. The first brick was a thoroughcensus of all matter in galaxies andgalaxy clusters using a variety of optical,x-ray and radio techniques. The un-equivocal conclusion was that the totalmass in chemical elements and dark mat-ter accounts for only about one third ofthe quantity that most theorists expect-ed—the so-called critical density.

Many cosmologists took this as a signthat the theorists were wrong. In that case,we would be living in an ever expandinguniverse where space is curved hyperbol-ically, like the horn on a trumpet. But thisinterpretation has been put to rest by mea-surements of hot and cold spots in thecosmic microwave background radia-tion, whose distribution has shown thatspace is flat and that the total energy den-sity equals the critical density. Putting thetwo observations together, simple arith-metic dictates the necessity for an addi-tional energy component to make up themissing two thirds of the energy density.

Whatever it is, the new componentmust be dark, neither absorbing nor emit-ting light, or else it would have been no-ticed long ago. In that way, it resembles

dark matter. But the new component—called dark energy—differs from darkmatter in one major respect: it must begravitationally repulsive. Otherwise itwould be pulled into galaxies and clus-ters, where it would affect the motion ofvisible matter. No such influence is seen.Moreover, gravitational repulsion re-solves the “age crisis” that plagued cos-mology in the 1990s. If one takes the cur-rent measurements of the expansion rateand assumes that the expansion has beendecelerating, the age of the universe is lessthan 12 billion years.

Yet evidence suggests that some starsin our galaxy are 15 billion years old. Bycausing the expansion rate of the universeto accelerate, repulsion brings the inferredage of the cosmos into agreement with theobserved age of celestial bodies [see “Cos-mological Antigravity,” on page 30].

The potential flaw in the argumentused to be that gravitational repulsionshould cause the expansion to accelerate,which had not been observed. Then, in1998, the last brick fell into place. Twoindependent groups used measurementsof distant supernovae to detect a changein the expansion rate. Both groups con-cluded that the universe is acceleratingand at just the pace predicted [see “Sur-veying Spacetime with Supernovae,” onpage 22].

All these observations boil down to

three numbers: the average density ofmatter (both ordinary and dark), the av-erage density of dark energy, and the cur-vature of space. Einstein’s equations dic-tate that the three numbers add up to thecritical density. The possible combina-tions of the numbers can be succinctlyrepresented on a triangular plot [see illus-tration on page 49]. The three distinctsets of observations—matter census, cos-mic microwave background, and super-novae—correspond to strips inside thetriangle. Remarkably, the three strips over-lap at the same position, which makes acompelling case for dark energy.

From Implosion to ExplosionOUR EVERYDAY EXPERIENCE is withordinary matter, which is gravitationallyattractive, so it is difficult to envisage howdark energy could gravitationally repel.The key feature is that its pressure is neg-ative. In Newton’s law of gravity, pressureplays no role; the strength of gravity de-pends only on mass. In Einstein’s law ofgravity, however, the strength of gravitydepends not just on mass but also on other forms of energy and on pressure. Inthis way, pressure has two effects: direct(caused by the action of the pressure on surrounding material) and indirect(caused by the gravitation that the pres-sure creates).

The sign of the gravitational force is


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JEREMIAH P. OSTRIKER and PAUL J. STEINHARDT, both professors at Princeton University,have been collaborating for the past seven years. Their prediction of accelerating expan-sion in 1995 anticipated groundbreaking supernova results by several years. Ostriker wasone of the first scientists to appreciate the prevalence of dark matter and the importanceof hot intergalactic gas. In 2000 he won the U.S. National Medal of Science. Steinhardt wasone of the originators of the theory of inflation and the concept of quasicrystals. He rein-troduced the term “quintessence” after his youngest son, Will, and daughter Cindy pickedit over several alternatives.

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Dark energy 70%

Exotic darkmatter 26% Ordinary

nonluminousmatter 3.5%

Ordinary visiblematter 0.5%

Radiation 0.005%P e r c e n t a g e s d o n o t a d d u p t o 1 0 0 b e c a u s e o f r o u n d i n g .

RECIPE FOR THE UNIVERSEThe main ingredient of the universe is dark energy, which consists of either thecosmological constant or the quantum field known as quintessence. The other ingredientsare dark matter (composed of exotic elementaryparticles), ordinary matter (both nonluminousand visible), and a trace amount of radiation.


determined by the algebraic combinationof the total energy density plus threetimes the pressure. If the pressure is pos-itive, as it is for radiation, ordinary mat-ter and dark matter, then the combina-tion is positive and gravitation is attrac-tive. If the pressure is sufficiently negative,the combination is negative and gravita-tion is repulsive. To put it quantitative-ly, cosmologists consider the ratio ofpressure to energy density, known as theequation of state, or w. For an ordinarygas, w is positive and proportional to thetemperature. But for certain systems, wcan be negative. If it drops below –1⁄3,gravity becomes repulsive.

Vacuum energy meets this condition(provided its density is positive). This isa consequence of the law of conservationof energy, according to which energy can-

not be destroyed. Mathematically the lawcan be rephrased to state that the rate ofchange of energy density is proportionalto w + 1. For vacuum energy—whose den-sity, by definition, never changes—thissum must be zero. In other words, wmust equal precisely –1. So the pressuremust be negative.

What does it mean to have negativepressure? Most hot gases have positivepressure; the kinetic energy of the atomsand radiation pushes outward on thecontainer. Note that the direct effect ofpositive pressure—to push—is the oppo-site of its gravitational effect—to pull. Butone can imagine an interaction amongatoms that overcomes the kinetic ener-gy and causes the gas to implode. Theimplosive gas has negative pressure. Aballoon of this gas would collapse in-

ward because the outside pressure (zeroor positive) would exceed the inside pres-sure (negative). Curiously, the direct ef-fect of negative pressure—implosion—

can be the opposite of its gravitational ef-fect—repulsion.

The gravitational effect is tiny for aballoon. But now imagine filling all ofspace with the implosive gas. Then thereis no bounding surface and no externalpressure. The gas still has negative pres-sure, but it has nothing to push against,so it exerts no direct effect. It has only thegravitational effect—namely, repulsion.The repulsion stretches space, increasingits volume and, in turn, the amount ofvacuum energy. The tendency to stretchis therefore self-reinforcing. The universeexpands at an accelerating pace. Thegrowing vacuum energy comes at theexpense of the gravitational field.

These concepts may sound strange,and even Einstein found them hard toswallow. He viewed the static universe,the original motivation for vacuum ener- D

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Attractive

Repulsive

Radiation Ordinary matter Quintessence(moderately negative pressure)

THE POWER OF POSITIVE (AND NEGATIVE) THINKINGWhether a lump of energy exerts a gravitationally attractive or repulsive force depends on itspressure. If the pressure is zero or positive, as it is for radiation or ordinary matter, gravity isattractive. (The downward dimples represent the potential energy wells.) Radiation has greaterpressure, so its gravity is more attractive. For quintessence, the pressure is negative and gravity isrepulsive (the dimples become hills).


gy, as an unfortunate error that ought tobe dismissed. But the cosmological con-stant, once introduced, would not fadeaway. Theorists soon realized that quan-tum fields possess a finite amount of vac-uum energy, a manifestation of quantumfluctuations that conjure up pairs of vir-tual particles from scratch. An estimateof the total vacuum energy produced byall known fields predicts a huge amount—120 orders of magnitude more than theenergy density in all other matter. That is,though it is hard to picture, the evanes-cent virtual particles should contribute apositive, constant energy density, whichwould imply negative pressure. But if this

estimate were true, an acceleration of epicproportions would rip apart atoms, starsand galaxies. Clearly, the estimate iswrong. One of the major goals of unifiedtheories of gravity has been to learn why.

One proposal is that some heretoforeundiscovered symmetry in fundamentalphysics results in a cancellation of large ef-fects, zeroing out the vacuum energy. Forexample, quantum fluctuations of virtualpairs of particles contribute positive ener-gy for particles with half-integer spin (likequarks and electrons) but negative energyfor particles with integer spin (like pho-tons). In standard theories, the cancella-tion is inexact, leaving behind an unac-ceptably large energy density. But physi-cists have been exploring models withso-called supersymmetry, a relation be-tween the two particle types that can leadto a precise cancellation. A serious flaw,though, is that supersymmetry would bevalid only at very high energies. Theoristsare working on a way of preserving theperfect cancellation even at lower energies.

Another thought is that the vacuumenergy is not exactly nullified after all.Perhaps there is a cancellation mecha-nism that is slightly imperfect. Instead ofmaking the cosmological constant exact-ly zero, the mechanism cancels only to120 decimal places. Then the vacuum en-ergy could constitute the missing two

thirds of the universe. That seems bizarre,though. What mechanism could possiblywork with such precision? Although thedark energy represents a huge amount ofmass, it is spread so thinly that its energyis less than four electron volts per cubicmillimeter—which, to a particle physicist,is unimaginably low. The weakest knownforce in nature involves an energy densi-ty 1,050 times greater.

Extrapolating back in time, vacuumenergy gets even more paradoxical. To-day matter and dark energy have compa-rable average densities. But billions ofyears ago, when they came into being,our universe was the size of a grapefruit,so matter was 100 orders of magnitudedenser. The cosmological constant, how-ever, would have had the same value as itdoes now. In other words, for every10,100 parts matter, physical processeswould have created one part vacuum en-ergy—a degree of exactitude that may bereasonable in a mathematical idealizationbut that seems ludicrous to expect fromthe real world. This need for almost su-pernatural fine-tuning is the principalmotivation for considering alternatives tothe cosmological constant.

FieldworkFORTUNATELY, vacuum energy is notthe only way to generate negative pres-


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ETERNAL EXPANSION

EVENTUAL COLLAPSEGROWING PAINSThe universe expands at different rates

depending on which form of energypredominates. Matter causes the growth to

decelerate, whereas the cosmological constantcauses it to accelerate. Quintessence is in the

middle: it forces the expansion to accelerate, butless rapidly. Eventually the acceleration may or

may not switch off (dashed lines).

Quintessence(highly negative pressure)


sure. Another means is an energy sourcethat, unlike vacuum energy, varies inspace and time—a realm of possibilitiesthat goes under the rubric of quintes-sence. For quintessence, w has no fixedvalue, but it must be less than –1⁄ 3 forgravity to be repulsive.

Quintessence may take many forms.The simplest models propose a quantumfield whose energy is varying so slowlythat it looks, at first glance, like a con-stant vacuum energy. The idea is bor-rowed from inflationary cosmology, inwhich a cosmic field known as the infla-ton drives expansion in the very early uni-verse using the same mechanism. The keydifference is that quintessence is muchweaker than the inflaton. This hypothe-sis was first explored a decade ago by

Christof Wetterich of the University ofHeidelberg and by Bharat Ratra, now atKansas State University, and P. James E.Peebles of Princeton University.

In quantum theory, physical processescan be described in terms either of fieldsor of particles. But because quintessencehas such a low energy density and variesso gradually, a particle of quintessencewould be inconceivably lightweight andlarge—the size of a supercluster of gal-axies. So the field description is rathermore useful. Conceptually, a field is acontinuous distribution of energy that as-signs to each point in space a numericalvalue known as the field strength. The en-ergy embodied by the field has a kineticcomponent, which depends on the timevariation of the field strength, and a po-tential component, which depends onlyon the value of the field strength. As thefield changes, the balance of kinetic andpotential energy shifts.

For vacuum energy, recall that thenegative pressure was the direct result ofthe conservation of energy, which dic-tates that any variation in energy densityis proportional to the sum of the energy

density (a positive number) and the pres-sure. For vacuum energy, the change iszero, so the pressure must be negative.For quintessence, the change is gradualenough that the pressure must still benegative, though somewhat less so. Thiscondition corresponds to having morepotential energy than kinetic energy.

Because its pressure is less negative,quintessence does not accelerate the uni-verse as strongly as vacuum energy does.Ultimately this will be how observers de-cide between the two. If anything, quin-tessence is more consistent with the avail-able data, but for now the distinction isnot statistically significant. Another dif-ference is that, unlike vacuum energy, thequintessence field may undergo all kindsof complex evolution. The value of w

may be positive, then negative, then pos-itive again. It may have different values indifferent places. Although the nonuni-formity is thought to be small, it may bedetectable by studying the cosmic micro-wave background radiation.

A further difference is that quintes-sence can be perturbed. Waves will prop-agate through it just as sound waves canpass through the air. In the jargon, quin-tessence is “soft.” Einstein’s cosmologi-cal constant is, in contrast, stiff—it can-not be pushed around. This raises an in-teresting issue. Every known form ofenergy is soft to some degree. Perhapsstiffness is an idealization that cannot ex-ist in reality, in which case the cosmolog-ical constant is an impossibility. Quin-tessence with w near −1 may be the clos-est reasonable approximation.

Quintessence on the BraneSAYING THAT quintessence is a field isjust the first step in explaining it. Wherewould such a strange field come from?Particle physicists have explanations forphenomena from the structure of atomsto the origin of mass, but quintessence is

something of an orphan. Modern theo-ries of elementary particles include manykinds of fields that might have the requi-site behavior, but not enough is knownabout their kinetic and potential energyto say which, if any, could produce neg-ative pressure today.

An exotic possibility is that quintes-sence springs from the physics of extra di-mensions. Over the past few decades, the-orists have been exploring string theory,which may combine general relativityand quantum mechanics in a unified the-ory of fundamental forces. An importantfeature of string models is that they pre-dict 10 dimensions. Four of these are ourfamiliar three spatial dimensions, plustime. The remaining six must be hidden.In some formulations, they are curled up

like a ball whose radius is too small to bedetected (at least with present instru-ments). An alternative idea is found in arecent extension of string theory, knownas M-theory, which adds an 11th dimen-sion: ordinary matter is confined to twothree-dimensional surfaces, known asbranes (short for membranes), separatedby a microscopic gap along the 11th di-mension [see “The Universe’s Unseen Di-mensions,” on page 66].

We are unable to see the extra di-mensions, but if they exist, we should beable to perceive them indirectly. In fact,the presence of curled-up dimensions ornearby branes would act just like a field.The numerical value that the field assignsto each point in space could correspondto the radius or gap distance. If the radiusor gap changes slowly as the universe ex-pands, it could exactly mimic the hypo-thetical quintessence field.

Whatever the origin of quintessence,its dynamism could solve the thornyproblem of fine-tuning. One way to lookat this issue is to ask why cosmic accel-eration has begun at this particular mo-ment in cosmic history. Created when


Quintessence might fuel a cyclic model in whichthe hot, homogeneous universe is made and remade eternally.


the universe was 10–35 second old, darkenergy must have remained in the shad-ows for nearly 10 billion years—a factorof more than 1050 in age. Only then, thedata suggest, did it overtake matter andcause the universe to begin accelerating.Is it not a coincidence that, just whenthinking beings evolved, the universesuddenly shifted into overdrive? Some-how the fates of matter and dark energyseem to be intertwined. But how?

If the dark energy is vacuum energy,the coincidence is almost impossible toaccount for. Some researchers, includingMartin Rees of the University of Cam-bridge and Steven Weinberg of the Uni-versity of Texas at Austin, have pursuedan anthropic explanation. Perhaps ouruniverse is just one among a multitude ofuniverses, in each of which the vacuumenergies takes on a different value. Uni-verses with vacuum energies much great-er than four electron volts per cubic mil-limeter might be more common, but theyexpand too rapidly to form stars, planetsor life. Universes with much smaller val-ues might be very rare. Our universewould have the optimal value. Only inthis “best of all worlds” could there ex-ist intelligent beings capable of contem-plating the nature of the universe. Butphysicists disagree whether the anthrop-ic argument constitutes an acceptable ex-planation [see “Exploring Our Universeand Others,” on page 82].

A more satisfying answer, whichcould involve a form of quintessenceknown as a tracker field, was studied byRatra and Peebles and by Steinhardt andIvaylo Zlatev and Limin Wang, then atthe University of Pennsylvania. The equa-tions that describe tracker fields haveclassical attractor behavior like thatfound in some chaotic systems. In suchsystems, motion converges to the sameresult for a wide range of initial condi-tions. A marble put into an empty bath-tub, for example, ultimately falls into thedrain whatever its starting place.

Similarly, the initial energy density ofthe tracker field does not have to be tunedto a certain value, because the field rapid-ly adjusts itself to that value. It locks intoa track on which its energy density re-mains a nearly constant fraction of the

density of radiation and matter. In thissense, quintessence imitates matter andradiation, even though its composition iswholly different. The mimicking occursbecause the radiation and matter densitydetermine the cosmic expansion rate,which, in turn, controls the rate at whichthe quintessence density changes. Oncloser inspection, one finds that the frac-tion is slowly growing. Only after manymillions or billions of years does quintes-sence catch up.

So why did quintessence catch upwhen it did? Cosmic acceleration couldjust as easily have begun in the distantpast or in the far future, depending on thechoices of constants in the tracker-fieldtheory. This brings us back to the coinci-dence. But perhaps some event in the rel-atively recent past unleashed the acceler-ation. Steinhardt, along with ChristianArmendáriz Picon, now at the Universityof Chicago, and Viatcheslav Mukhanovof Ludwig Maximilians University in

Munich, has proposed one such recentevent: the transition from radiation dom-ination to matter domination.

According to the big bang theory, theenergy of the universe used to reside main-ly in radiation. As the universe cooled,however, the radiation lost energy fasterthan ordinary matter did. By the time theuniverse was a few tens of thousands ofyears old—a relatively short time ago inlogarithmic terms—the energy balancehad shifted in favor of matter. Thischange marked the beginning of the mat-ter-dominated epoch of which we are thebeneficiaries. Only then could gravity be-gin to pull matter together to form galax-ies and larger-scale structures. At thesame time, the expansion rate of the uni-verse underwent a change.

In a variation on the tracker models,this transformation triggered a series ofevents that led to cosmic acceleration to-day. Throughout most of the history ofthe universe, quintessence tracked the ra-


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SEEING WILL BE BELIEVINGSupernova data may be one way to decide between quintessence and the cosmological constant. The latter makes the universe speed up faster, so supernovae at a given redshift would be fartheraway and hence dimmer. Existing telescopes (data shown in gray) cannot tell the two cases apart,but the proposed Supernova Acceleration Probe should be able to. The supernova magnitudespredicted by four models are shown in different colors.

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diation energy, remaining an insignifi-cant component of the cosmos. Butwhen the universe became matter-dom-inated, the change in the expansion ratejolted quintessence out of its copycat be-havior. Instead of tracking radiation oreven matter, the pressure of quintessenceswitched to a negative value. Its densitystayed nearly fixed and ultimately over-took the decreasing matter density. Inthis picture, the fact that thinking beingsand cosmic acceleration came into exis-tence at nearly the same time is not a coincidence. Both the formation of starsand planets necessary to support lifeand the transformation of quintessenceinto a negative-pressure componentwere triggered by the onset of matterdomination.

Looking to the FutureIN THE SHORT TERM, the focus ofcosmologists will be to detect the exis-tence of quintessence. It has observable

consequences. Because its value of w dif-fers from that of vacuum energy, it pro-duces a different rate of cosmic accelera-tion. More precise measurements of su-pernovae over a longer span of distancesmay separate the two cases. Astron-omers have proposed two new observa-tories—the orbiting Supernova Acceler-ation Probe and the Earth-based Large-Aperture Synoptic Survey Telescope—toresolve the issue. Differences in accelera-tion rate also produce small differencesin the angular size of hot and cold spotsin the cosmic microwave background ra-diation, as the Microwave AnisotropyProbe (MAP) and Planck spacecraftshould be able to detect.

Other tests measure how the numberof galaxies varies with increasing red-shift to infer how the expansion rate ofthe universe has changed with time. Aground-based project known as the DeepExtragalactic Evolutionary Probe willlook for this effect.

Over the longer term, all of us will beleft to ponder the profound implicationsof these revolutionary discoveries. Theylead to a sobering new interpretation ofour place in cosmic history. In the begin-ning (or at least at the earliest time forwhich we have any clue), there was infla-tion, an extended period of acceleratedexpansion during the first instants afterthe big bang. Space back then was near-ly devoid of matter, and a quintessence-like quantum field with negative pressureheld sway. During that period, the uni-verse expanded by a greater factor than ithas during the 15 billion years since in-flation ended. At the end of inflation, thefield decayed to a hot gas of quarks, glu-ons, electrons, light, and dark energy.

For thousands of years, space was sothick with radiation that atoms, let alonelarger structures, could not form. Thenmatter took control. The next stage—ourepoch—has been one of steady cooling,condensation and the evolution of intri-

cate structure of ever increasing size. Butthis period is coming to an end. Cosmicacceleration is back. The universe as weknow it, with shining stars, galaxies andclusters, appears to have been a brief in-terlude. As acceleration takes hold overthe next tens of billions of years, the mat-ter and energy in the universe will becomemore and more diluted and space willstretch too rapidly to enable new struc-tures to form. Living things will find thecosmos increasingly hostile [see “TheFate of Life in the Universe,” on page 50].If the acceleration is caused by vacuumenergy, then the cosmic story is complete:the planets, stars and galaxies we see to-day are the pinnacle of cosmic evolution.

But if the acceleration is caused byquintessence, the ending has yet to bewritten. The universe might accelerateforever, or the quintessence could decayinto new forms of matter and radiation,repopulating the universe. Because thedark energy density is so small, one might

suppose that the material derived from itsdecay would have too little energy to doanything of interest. Under some circum-stances, however, quintessence could de-cay through the nucleation of bubbles.The bubble interior would be a void, butthe bubble wall would be the site of vig-orous activity. As the wall moved out-ward, it would sweep up all the energyderived from the decay of quintessence.Occasionally, two bubbles would collidein a fantastic fireworks display. In theprocess, massive particles such as protonsand neutrons might arise—perhaps starsand planets.

To future inhabitants, the universewould look highly inhomogeneous, withlife confined to distant islands surround-ed by vast voids. Would they ever figureout that their origin was the homoge-neous and isotropic universe we see aboutus today? Would they ever know that theuniverse had once been alive and thendied, only to be given a second chance?

Or perhaps a more radical revision ofcosmic history is in store. Inspired by therecent observations of cosmic accelera-tion, Steinhardt and Neil Turok of theUniversity of Cambridge have proposeda “cyclical universe” model in whichquintessence is center stage and inflationis excised altogether. In this picture, spaceand time exist forever. The universe un-dergoes an endless sequence of cycles inwhich it contracts in a big crunch andreemerges in an expanding big bang,with trillions of years of evolution in be-tween. During the first 15 billion years ofeach cycle, the universe is dominated byradiation and matter, and as the universecools, galaxies and stars form. Then, justas we are seeing today, quintessence ini-tiates an extended period of acceleratedexpansion that empties the universe ofthe matter and entropy created in theprevious cycle. Quintessence plays theessential role of making the universe homogeneous and at the same time flat-

Special survey instruments, plus new tests,will tell us which future is ours.


tens the spatial geometry—two of thefunctions that are usually attributed toinflation.

In addition, fluctuations in the quin-tessence field eventually form the seedsfor galaxy formation after the bang, thethird function played by inflation. As thequintessence field evolves, its density andpressure change until the field ceases tocause acceleration and instead initiates aperiod of contraction. At the crunch,some of the energy of the quintessencefield is converted into the matter and ra-diation that fuel the bang and a new pe-riod of expansion, cooling and structureformation. Notably, the temperatureand density rise to a large but finite den-sity. So the model also avoids the infini-ties of the conventional big bang view.The hot, homogeneous universe is madeand remade eternally.

The cyclic scenario has a natural in-terpretation in terms of the superstringpicture of branes and extra dimensions.The cycles can be described as an infinite,periodic sequence of collisions betweenbranes. Each collision creates a bang inwhich new matter and radiation are cre-ated. The radiation and matter cause thebranes to stretch—the usual period ofcosmic expansion. Yet there is also aforce between the branes that con-tributes a positive potential energy to theuniverse when the branes are far apart.In this scenario, quintessence is simplythis potential energy. After 15 billionyears of expansion, the interbrane po-tential energy dominates the universeand a period of cosmic acceleration be-gins. The branes stretch sufficiently to di-lute the density of matter and radiationand flatten any curvature or wrinkles inthe branes’ surfaces.

The branes move together slowly, butas they approach, the potential energyeventually decreases from a positive to anegative value. The quintessence fieldnow causes the stretching to stop and thebranes to speed toward collision. The col-lision and bounce correspond to the re-versal from contraction to expansion. Yetonly the extra-dimensions componentcollapses and reappears. The usual three-dimensions component remains infinite.Hence, the density of matter on the

branes remains small and dilute even atthe crunch. When the two branes bounceapart, the potential energy is restored toits original value and quintessence is re-created in preparation for the next cycle.

Experiments may soon give us someidea which future is ours. We trust thatimproved accuracy of the classic cosmo-logical tests, plus specially designed sur-vey instruments and some new tests (pos-

sibly using gravitational lensing), willmake this possible. Will it be the dead endof vacuum energy or the untapped po-tential of quintessence? Ultimately the an-swer depends on whether quintessencehas a place in the basic workings of na-ture—the realm, perhaps, of string theory.Our place in cosmic history hinges on theinterplay between the science of the verybig and that of the very small.


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Cosmological Imprint of an Energy Component with General Equation of State. Robert R. Caldwell,Rahul Dave and Paul J. Steinhardt in Physical Review Letters, Vol. 80, No. 8, pages 1582–1585;February 23, 1998. Available at xxx.lanl.gov/abs/astro-ph/9708069

Cosmic Concordance and Quintessence. Limin Wang, R. R. Caldwell, J. P. Ostriker and Paul J.Steinhardt in Astrophysical Journal, Vol. 530, No. 1, Part 1, pages 17–35; February 10, 2000.Available at astro-ph/9901388

Dynamical Solution to the Problem of a Small Cosmological Constant and Late-Time CosmicAcceleration. C. Armendáriz Picon, V. Mukhanov and Paul J. Steinhardt in Physical Review Letters,Vol. 85, No. 21, pages 4438–4441; November 20, 2000. Available at astro-ph/0004134

Why Cosmologists Believe the Universe Is Accelerating. Michael S. Turner in Type Ia Supernovae:Theory and Cosmology. Edited by Jens C. Niemeyer and James W. Truran. Cambridge UniversityPress, 2000. Available at astro-ph/9904049

A Cyclic Model of the Universe. Paul J. Steinhardt and Neil Turok in Science, Vol. 296, No. 5572,pages 1436–1439; 2002.


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COSMIC TRIANGLEIn this graph of cosmological observations, the axes represent possible values of three keycharacteristics of the universe. If the universe is flat, as inflationary theory suggests, the differenttypes of observations (colored areas) and the zero-curvature line (red line) should overlap. Atpresent, the microwave background data produce a slightly better overlap if dark energy consists of quintessence (dashed outline) rather than the cosmological constant (green area).


BY LAWRENCE M. KRAUSS AND GLENN D. STARKMAN

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Eternal life is a core belief of many of theworld’s religions. Usually it is extolled as aspiritual Valhalla, an existence without pain,death, worry or evil, a world removed fromour physical reality. But there is another sortof eternal life that we hope for, one in the tem-

poral realm. In the conclusion to On the Origin of Spe-cies, Charles Darwin wrote: “As all the living forms of lifeare the lineal descendants of those which lived before the

Cambrian epoch, we may feel certain that the ordinarysuccession by generation has never once been broken.. . .Hence we may look with some confidence to a secure fu-ture of great length.” The sun will eventually exhaust itshydrogen fuel, and life as we know it on our home planetwill eventually end, but the human race is resilient. Ourprogeny will seek new homes, spreading into every cornerof the universe just as organisms have colonized every pos-sible niche of the earth. Death and evil will take their toll,

universeof life in thefatethe

BILLIONS OF YEARS AGO THE UNIVERSE WAS TOO

HOT FOR LIFE TO EXIST. COUNTLESS AEONS FROM NOW,

IT WILL BECOME SO COLD AND EMPTY THAT LIFE,

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Cosmic inflationSpace and time disentangle

10–51 year since big bang 10–44

MILESTONES ON THE ROAD TO ETERNITY range from the big bang throughthe birth and death of stars (time line below). As the last stars wane,intelligent beings will need to find new sources of energy, such as cosmicstrings (illustration above). Unfortunately, natural processes—such asoutbreaks of black holes—will erode these linear concentrations of energy,

eventually forcing life-forms to seek sustenance elsewhere, if they can findit. Because the governing processes of the universe act on widely varyingtimescales, the time line is best given a logarithmic scale. If the universe isnow expanding at an accelerating rate, additional effects (shown on timeline in blue) will make life even more miserable.


pain and worry may never go away, but somewhere we expectthat some of our children will carry on.

Or maybe not. Remarkably, even though scientists fully un-derstand neither the physical basis of life nor the unfolding ofthe universe, they can make educated guesses about the destinyof living things. Cosmological observations now suggest thatthe universe will continue to expand forever—rather than, asscientists once thought, expanding to a maximum size and thenshrinking. Therefore, we are not doomed to perish in a fiery“big crunch” in which any vestige of our current or future civ-ilization would be erased. At first glance, eternal expansion iscause for optimism. What could stop a sufficiently intelligentcivilization from exploiting the endless resources to surviveindefinitely?

The Deserts of Vast EternityYET LIFE THRIVES ON energy and information, and verygeneral scientific arguments hint that only a finite amount ofenergy and a finite amount of information can be amassed ineven an infinite period. For life to persist, it would have tomake do with dwindling resources and limited knowledge. Wehave concluded that no meaningful form of consciousnesscould exist forever under these conditions.

Over the past century, scientific eschatology has swungbetween optimism and pessimism. Not long after Darwin’sconfident prediction, Victorian-era scientists began to fretabout the “heat death,” in which the whole cosmos wouldcome to a common temperature and thereafter be incapable ofchange. The discovery of the expansion of the universe in the1920s allayed this concern, because expansion prevents the uni-verse from reaching such an equilibrium. But few cosmologiststhought through the other implications for life in an ever ex-panding universe, until a classic paper in 1979 by physicistFreeman Dyson of the Institute for Advanced Study in Prince-ton, N.J., itself motivated by earlier work by Jamal Islam, nowat the University of Chittagong in Bangladesh. Since Dyson’spaper, physicists and astronomers have periodically reexam-ined the topic [see “The Future of the Universe,” by Duane A.Dicus, John R. Letaw, Doris C. Teplitz and Vigdor L. Teplitz;Scientific American, March 1983]. In 1998, spurred on bynew observations that suggest a drastically different long-termfuture for the universe than that previously envisaged, we be-gan to take another look.

Over the past 12 billion years or so, the universe has passedthrough many stages. At the earliest times for which scientistsnow have empirical information, it was incredibly hot and

52 S C I E N T I F I C A M E R I C A N U p d a t e d f r o m t h e N o v e m b e r 19 9 9 i s s u e

ENERGY COLLECTION STRATEGY devised by physicist Steven Frautschi ofCaltech illustrates how difficult it will be to survive in the far future, 10100 or soyears from now. In many cosmological scenarios, resources multiply as theuniverse—and any arbitrary reference sphere within it (blue sphere)—expands and an increasing fraction of it becomes observable (red sphere).

A civilization could use a black hole to convert matter—plundered from itsempire (green sphere)—into energy. But as the empire grows, the cost ofcapturing new territory increases; the conquest can barely keep pace with thedilution of matter. In fact, matter will become so diluted that the civilizationwill not be able to safely build a black hole large enough to collect it.

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dense. Gradually, it expanded and cooled. For hundreds ofthousands of years, radiation ruled; the famous cosmic micro-wave background radiation is thought to be a vestige of thisera. Then matter started to dominate, and progressively largerastronomical structures condensed out. Now, if recent cosmo-logical observations are correct, the expansion of the universeis beginning to accelerate—a sign that a strange new type of en-ergy, perhaps springing from space itself, may be taking over.

Life as we know it depends on stars. But stars inevitably die,and their birth rate has declined dramatically since an initialburst about 10 billion years ago. About 100 trillion years fromnow, the last conventionally formed star will wink out, and anew era will commence. Processes currently too slow to be no-ticed will become important: the dispersal of planetary systemsby stellar close encounters, the possible decay of ordinary andexotic matter, the slow evaporation of black holes.

Assuming that intelligent life can adapt to the changing cir-cumstances, what fundamental limits does it face? In an eter-nal universe, potentially of infinite volume, one might hope thata sufficiently advanced civilization could collect an infiniteamount of matter, energy and information. Surprisingly, thisis not true. Even after an eternity of hard and well-planned la-bor, living beings could accumulate only a finite number of par-ticles, a finite quantity of energy and a finite number of bits ofinformation. What makes this failure all the more frustratingis that the number of available particles, ergs and bits may growwithout bound. The problem is not necessarily the lack of re-sources but rather the difficulty in collecting them.

The culprit is the very thing that allows us to contemplatean eternal tenure: the expansion of the universe. As the cosmos

grows in size, the average density of ordinary sources of ener-gy declines. Doubling the radius of the universe decreases thedensity of atoms eightfold. For light waves, the decline is evenmore precipitous. Their energy density drops by a factor of 16because the expansion stretches them and thereby saps their en-ergy [see illustration at left].

As a result of this dilution, resources become ever moretime-consuming to collect. Intelligent beings have two distinctstrategies: let the material come to them or try to chase it down.For the former, the best approach in the long run is to let grav-ity do the work. Of all the forces of nature, just gravity and elec-tromagnetism can draw things in from arbitrarily far away. Butthe latter gets screened out: oppositely charged particles bal-ance one another, so that the typical object is neutral and henceimmune to long-range electrical and magnetic forces. Gravity,on the other hand, cannot be screened out, because particles ofmatter and radiation only attract gravitationally; they do notrepel.

Surrender to the VoidEVEN GRAVITY, however, must contend with the expansionof the universe, which pulls objects apart and thereby weakenstheir mutual attraction. In all but one scenario, gravity even-tually becomes unable to pull together larger quantities of ma-terial. Indeed, our universe may have already reached thispoint; clusters of galaxies may be the largest bodies that grav-ity will ever be able to bind together [see “The Evolution ofGalaxy Clusters,” by J. Patrick Henry, Ulrich G. Briel and HansBöhringer; Scientific American, December 1998]. The loneexception occurs if the universe is poised between expansionand contraction, in which case gravity continues indefinitely toassemble increasingly greater amounts of matter. But that sce-nario is now thought to contradict observations, and in any

LAWRENCE M. KRAUSS and GLENN D. STARKMAN consider their ru-minations on the future of life to be a natural extension of their in-terest in the fundamental workings of the universe. Krauss’sbooks on the predictions of science fiction, The Physics of StarTrek and Beyond Star Trek, have a similar motivation. The chair ofthe physics department at Case Western Reserve University,Krauss was among the first cosmologists to argue forcefully thatthe universe is dominated by a cosmological constant—a viewnow widely shared. Starkman, also a professor at Case Western,is perhaps best known for his work on the topology of the universe.Both authors are frustrated optimists. They have sought waysthat life could persist forever, to no avail. Nevertheless, they main-tain the hope that the Cleveland Indians will win the World Seriesin the ample time that remains.

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DILUTION of the cosmos by the expansion of space affects different formsof energy in different ways. Ordinary matter (orange) thins out in directproportion to volume, whereas the cosmic background radiation (purple)weakens even faster as it is stretched from light into microwaves andbeyond. The energy density represented by a cosmological constant (blue)does not change, at least according to present theories.

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event it poses its own difficulty: after 1033 years or so, the ac-cessible matter will become so concentrated that most of it willcollapse into black holes, sweeping up any life-forms. Being in-side a black hole is not a happy condition. On the earth, allroads may lead to Rome, but inside a black hole, all roads leadin a finite amount of time to the center of the hole, where deathand dismemberment are certain.

Sadly, the strategy of actively seeking resources fares no bet-ter than the passive approach does. The expansion of the uni-verse drains away kinetic energy, so prospectors would have tosquander their booty to maintain their speed. Even in the mostoptimistic scenario—in which the energy is traveling towardthe scavenger at the speed of light and is collected withoutloss—a civilization could garner limitless energy only in or neara black hole. The latter possibility was explored by StevenFrautschi of the California Institute of Technology in 1982. Heconcluded that the energy available from the holes would dwin-dle more quickly than the costs of scavenging [see illustrationon page 52]. We recently reexamined this possibility and foundthat the predicament is even worse than Frautschi thought. Thesize of a black hole required to sweep up energy forever exceedsthe extent of the visible universe.

The cosmic dilution of energy is truly dire if the universe isexpanding at an accelerating rate. All distant objects that arecurrently in view will eventually move away from us faster thanthe speed of light and, in doing so, disappear from view. Thetotal resources at our disposal are therefore limited by what wecan see today, at most [see box at right].

Not all forms of energy are equally subject to the dilution.The universe might, for example, be filled with a network ofcosmic strings—infinitely long, thin concentrations of energythat could have developed as the early universe cooled un-evenly. The energy per unit length of a cosmic string remainsunchanged despite cosmic expansion [see “Cosmic Strings,” byAlexander Vilenkin; Scientific American, December 1987].Intelligent beings might try to cut one, congregate around theloose ends and begin consuming it. If the string network isinfinite, they might hope to satisfy their appetite forever. Theproblem with this strategy is that whatever life-forms can do,natural processes can also do. If a civilization can figure out away to cut cosmic strings, then the string network will fall apartof its own accord. For example, black holes may spontaneouslyappear on the strings and devour them. Therefore, the beingscould swallow only a finite amount of string before runninginto another loose end. The entire string network would even-tually disappear, leaving the civilization destitute.

What about mining the quantum vacuum? After all, thecosmic acceleration may be driven by the so-called cosmolog-ical constant, a form of energy that does not dilute as the uni-verse expands [see “Cosmological Antigravity,” on page 30].

If this is so, empty space is filled with a bizarre type of radia-tion, called Gibbons-Hawking or de Sitter radiation. Alas, itis impossible to extract energy from this radiation for usefulwork. If the quantum vacuum yielded up energy, it would dropinto a lower energy state, yet the vacuum is already the lowestenergy state there is.

No matter how clever we try to be and how cooperative theuniverse is, we will someday have to confront the finiteness ofthe resources at our disposal. Even so, are there ways to copeforever?


The Worst of All Possible UniversesAMONG ALL THE SCENARIOS for an eternally expanding universe,the one dominated by the so-called cosmological constant is thebleakest. Not only is it unambiguous that life cannot surviveeternally in such a universe, but the quality of life will quicklydeteriorate as well. So if recent observations that the expansion isaccelerating are borne out [see “Surveying Spacetime withSupernovae,” on page 22], humankind could face a grim future.

Cosmic expansion carries objects away from one another unlessthey are bound together by gravity or another force. In our case, theMilky Way is part of a larger cluster of galaxies. About 10 millionlight-years across, this cluster remains a cohesive whole, whereasgalaxies beyond it are whisked away as intergalactic spaceexpands. The relative velocity of these distant galaxies isproportional to their distance. Beyond a certain distance called thehorizon, the velocity exceeds the speed of light (which is allowed inthe general theory of relativity because the velocity is imparted bythe expansion of space itself). We can see no farther.

If the universe has a cosmological constant with a positivevalue, as the observations suggest, the expansion is accelerating:galaxies are beginning to move apart ever more rapidly. Theirvelocity is still proportional to their distance, but the constant ofproportionality remains constant rather than decreasing with time,as it does if the universe decelerates. Consequently, galaxies thatare now beyond our horizon will forever remain out of sight. Even thegalaxies we can currently see—except for those in the local cluster—

will eventually attain the speed of light and vanish from view. Theacceleration, which resembles inflation in the very early universe,began when the cosmos was about half its present age.

The disappearance of distant galaxies will be gradual. Their lightwill stretch out until it becomes undetectable. Over time, the amountof matter we can see will decrease, and the number of worlds ourstarships can reach will diminish. Within two trillion years, wellbefore the last stars in the universe die, all objects outside our owncluster of galaxies will no longer be observable or accessible. Therewill be no new worlds to conquer, literally. We will truly be alone inthe universe. —L.M.K. and G.D.S.

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Black holes consume galaxiesGalactic fuel exhausted at current rate of consumption


The obvious strategy is to learn to make do with less, ascheme first discussed quantitatively by Dyson. In order to re-duce energy consumption and keep it low despite exertion, wewould eventually have to reduce our body temperature. Onemight speculate about genetically engineered humans whofunction at somewhat lower temperatures than 310 kelvins(98.6 degrees Fahrenheit). Yet the human body temperaturecannot be reduced arbitrarily; the freezing point of blood is afirm lower limit. Ultimately, we will need to abandon our bod-ies entirely.

Though futuristic, the idea of shedding our bodies presents

no fundamental difficulties. It presumes only that conscious-ness is not tied to a particular set of organic molecules butrather can be embodied in a multitude of different forms, fromcyborgs to sentient interstellar clouds [see “Will Robots Inher-it the Earth?” by Marvin Minsky; Scientific American, Oc-tober 1994]. Most modern philosophers and cognitive scien-tists regard conscious thought as a process that a computercould perform. The details need not concern us here (which isconvenient, as we are not competent to discuss them). We stillhave many billions of years to design new physical incarnationsto which we will someday transfer our conscious selves. These


EXPANDING UNIVERSE looks dramatically different depending on whether thegrowth is decelerating (upper sequence) or accelerating (lower sequence).In both these cases, the universe is infinite, but any patch of space—demarcated by a reference sphere that represents the distance to particulargalaxies—enlarges (blue sphere). Humans can see only a limited volume of

the universe around them, which grows steadily as light signals have time to propagate (red sphere). If expansion is decelerating, we can see anincreasing fraction of the cosmos. More and more galaxies fill the sky. But ifexpansion is accelerating, we can see a decreasing fraction of the cosmos.Space seems to empty out.

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new “bodies” will be required to operate at cooler tempera-tures and at lower metabolic rates—that is, at lower rates ofenergy consumption.

Dyson showed that if organisms could slow their metab-olism as the universe cooled, they could arrange to consume afinite total amount of energy over all of eternity. Although thelower temperatures would also slow consciousness—the num-ber of thoughts per second—the rate would remain largeenough for the total number of thoughts, in principle, to be un-limited. In short, intelligent beings could survive forever, notjust in absolute time but in subjective time as well. As long asorganisms were guaranteed to have an infinite number ofthoughts, they would not mind a languid pace of life. Whenbillions of years stretch out before you, what’s the rush?

At first glance, this might look like a case of something fornothing. But the mathematics of infinity can defy intuition. Foran organism to maintain the same degree of complexity, Dysonargued, its rate of information processing must be directly pro-portional to body temperature, whereas the rate of energy con-sumption is proportional to the square of the temperature (theadditional factor of temperature comes from basic thermody-namics). Therefore, the power requirements slacken faster thancognitive alacrity does [see illustration at right]. At 310 kelvins,the human body expends approximately 100 watts. At 155kelvins, an equivalently complex organism could think at halfthe speed but consume a quarter of the power. The trade-offis acceptable because physical processes in the environmentslow down at a similar rate.

To Sleep, to DieUNFORTUNATELY, there is a catch. Most of the power is dis-sipated as heat, which must escape—usually by radiatingaway—if the object is not to heat up. Human skin, for exam-ple, glows in infrared light. At very low temperatures, the mostefficient radiator would be a dilute gas of electrons. Yet theefficiency of even this optimal radiator declines as the cube ofthe temperature, faster than the decrease in the metabolic rate.A point would come when organisms could not lower theirtemperature further. They would be forced instead to reducetheir complexity—to dumb down. Before long, they could nolonger be regarded as intelligent.

To the timid, this might seem like the end. But to compen-sate for the inefficiency of radiators, Dyson boldly devised astrategy of hibernation. Organisms would spend only a smallfraction of their time awake. While sleeping, their metabolicrates would drop, but—crucially—they would continue to dis-sipate heat. In this way, they could achieve an ever lower av-erage body temperature [see illustration on opposite page]. Infact, by spending an increasing fraction of their time asleep,

they could consume a finite amount of energy yet exist foreverand have an infinite number of thoughts. Dyson concluded thateternal life is indeed possible.

Since his original paper, several difficulties with his planhave emerged. For one, Dyson assumed that the average tem-perature of deep space—currently 2.7 kelvins, as set by the cos-mic microwave background radiation—would always decreaseas the cosmos expands, so that organisms could continue to de-crease their temperature forever. But if the universe has a cos-mological constant, the temperature has an absolute floor fixedby the Gibbons-Hawking radiation. For current estimates ofthe value of the cosmological constant, this radiation has an ef-fective temperature of about 10–29 kelvin. As was noted inde-pendently by cosmologists J. Richard Gott II, John Barrow,Frank Tipler and us, once organisms had cooled to this level,they could not continue to lower their temperature in order toconserve energy.

The second difficulty is the need for alarm clocks to wakethe organisms periodically. These clocks would have to oper-ate reliably for longer and longer times on less and less ener-gy. Quantum mechanics suggests that this is impossible. Con-sider, for example, an alarm clock that consists of two smallballs that are taken far apart and then aimed at each other andreleased. When they collide, they ring a bell. To lengthen thetime between alarms, organisms would release the balls at aslower speed. But eventually the clock will run up against con-straints from Heisenberg’s uncertainty principle, which pre-vents the speed and position of the balls from both beingspecified to arbitrary precision. If one or the other is sufficient-


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ETERNAL LIFE ON FINITE ENERGY? If a new form of life could lower its bodytemperature below the human value of 310 kelvins (98.6 degreesFahrenheit), it would consume less power, albeit at the cost of thinkingmore sluggishly (left graph). Because metabolism would decline fasterthan cognition, the life-form could arrange to have an infinite number ofthoughts on limited resources. One caveat is that its ability to dissipatewaste heat would also decline, preventing it from cooling below about

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ly inaccurate, the alarm clock will fail, and hibernation willturn into eternal rest.

One might imagine other alarm clocks that could foreverremain above the quantum limit and might even be integratedinto the organism itself. Nevertheless, no one has yet come upwith a specific mechanism that could reliably wake an organ-ism while consuming finite energy.

The Eternal Recurrence of the SameTHE THIRD AND MOST general doubt about the long-term viability of intelligent life involves fundamental limitations oncomputation. Computer scientists once thought it was impos-sible to compute without expending a certain minimumamount of energy per operation, an amount that is directly pro-portional to the temperature of the computer. Then, in the ear-ly 1980s, researchers realized that certain physical processes,such as quantum effects or the random Brownian motion of aparticle in a fluid, could serve as the basis for a lossless com-puter [see “The Fundamental Physical Limits of Computa-tion,” by Charles H. Bennett and Rolf Landauer; ScientificAmerican, July 1985].

Such computers could operate with an arbitrarily smallamount of energy. To use less, they simply slow down—atrade-off that eternal organisms may be able to make. Thereare only two conditions. First, they must remain in thermalequilibrium with their environment. Second, they must neverdiscard information. If they did, the computation would be-come irreversible, and thermodynamically an irreversible pro-cess must dissipate energy.

Unhappily, those conditions become insurmountable in anexpanding universe. As cosmic expansion dilutes and stretch-es the wavelength of light, organisms become unable to emit orabsorb the radiation they would need to establish thermal equi-librium with their surroundings. And with a finite amount ofmaterial at their disposal, and hence a finite memory, they

would eventually have to forget an old thought in order to havea new one. What kind of perpetual existence could such or-ganisms have, even in principle? They could collect just a finitenumber of particles and a finite amount of information. Thoseparticles and bits could be configured in just a finite numberof ways. Because thoughts are the reorganization of informa-tion, finite information implies a finite number of thoughts. Allorganisms would ever do is relive the past, having the samethoughts over and over again. Eternity would become a prison,rather than an endlessly receding horizon of creativity and ex-ploration. It might be nirvana, but would it be living?

It is only fair to point out that Dyson has not given up. Inhis correspondence with us, he has suggested that life canavoid the quantum constraints on energy and information by,for example, growing in size or using different types of mem-ory. As he intriguingly puts it, the question is whether life is“analog” or “digital”—that is, whether continuum physics orquantum physics sets its limits. We believe that over the longhaul, life is digital.

Is there any other hope for eternal life? Quantum mechan-ics, which we argue puts such unbending limits on life, mightcome to its rescue in another guise. For instance, if the quan-tum mechanics of gravity allows the existence of stable worm-holes, life-forms might circumvent the barriers erected by thespeed of light, visit parts of the universe that are otherwise in-accessible, and collect infinite amounts of energy and informa-tion. Or perhaps they could construct “baby” universes [see“The Self-Reproducing Inflationary Universe,” by AndreiLinde; Scientific American, November 1994] and sendthemselves—or at least a set of instructions that could be usedto reconstitute themselves—through to the baby universe. Inthat way, life could carry on.

The ultimate limits on life will in any case become signifi-cant only on timescales that are truly cosmic. Still, to some itmay seem disturbing that life, certainly in its physical incarna-tion, must come to an end. But to us, it is remarkable that evenwith our limited knowledge, we can draw conclusions aboutsuch grand issues. Perhaps being cognizant of our fascinatinguniverse and our destiny within it is a greater gift than beingable to inhabit it forever.


Time without End: Physics and Biology in an Open Universe. Freeman J.Dyson in Reviews of Modern Physics, Vol. 51, No. 3, pages 447–460; July 1979.

The Anthropic Cosmological Principle. John D. Barrow and Frank J. Tipler.Oxford University Press, 1988.

The Last Three Minutes: Conjectures about the Ultimate Fate of theUniverse. Paul C. W. Davies. HarperCollins, 1997.

The Five Ages of the Universe: Inside the Physics of Eternity. Fred Adams and Greg Laughlin. Free Press, 1999.

Quintessence: The Mystery of the Missing Mass. Lawrence M. Krauss.Basic Books, 1999.

Life, the Universe, and Nothing: Life and Death in an Ever-ExpandingUniverse. Lawrence M. Krauss and Glenn D. Starkman in AstrophysicalJournal, Vol. 531, pages 22–30; 2000. Available atxxx.lanl.gov/abs/astro-ph/9902189


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10–13 kelvin. Hibernation (right graph) might eliminate the problem of heatdisposal. As the life-form cooled, it would spend an increasing fraction of itstime dormant, further reducing its average metabolic rate and cognitivespeed. In this way, the power consumption could always remain lower thanthe maximum rate of heat dissipation, while still allowing for an infinitenumber of thoughts. But such a scheme might run afoul of other problems,such as quantum limits.


Looking up at the sky on aclear night, we feel we cansee forever. There seems tobe no end to the stars andgalaxies; even the darknessin between them is filled

with light if only we stare through a sen-sitive enough telescope. In truth, ofcourse, the volume of space we can ob-serve is limited by the age of the universeand the speed of light. But given enoughtime, could we not peer ever farther, al-ways encountering new galaxies andphenomena?

Maybe not. Like a hall of mirrors,the apparently endless universe might bedeluding us. The cosmos could, in fact,be finite. The illusion of infinity wouldcome about as light wrapped all theway around space, perhaps morethan once—creating multiple im-ages of each galaxy. Our ownMilky Way galaxy would be noexception; bizarrely, the skiesmight even contain facsimiles ofthe earth at some earlier era. Astime marched on, astronomerscould watch the galaxies developand look for new mirages. But even-tually no new space would enter intotheir view. They would have seen it all.

The question of a finite or infinite universe is one of the old-est in philosophy. A common misconception is that it hasalready been settled in favor of the latter. The reasoning, oftenrepeated in textbooks, draws an unwarranted conclusion from

58 S C I E N T I F I C A M E R I C A N U p d a t e d f r o m t h e A p r i l 1 9 9 9 i s s u e

“INFINITY BOX” evokes a finite cosmos thatlooks endless. The box contains only three

balls, yet the mirrors that line its walls producean infinite number of images. Of course, in thereal universe there is no boundary from which

light can reflect. Instead a multiplicity ofimages could arise as light rays wrap around

the universe again and again. From the patternof repeated images, one could deduce the

universe’s true size and shape.

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Einstein’s general theory of relativity. According to relativity,space is a dynamic medium that can curve in one of three ways,depending on the distribution of matter and energy within it.Because we are embedded in space, we cannot see the flexuredirectly but rather perceive it as gravitational attraction andgeometric distortion of images. To determine which of the threegeometries our universe has, astronomers have been measur-ing the density of matter and energy in the cosmos. It nowappears to be too low to force space to arch back on itself—a“spherical” geometry. Therefore, space must have either thefamiliar Euclidean geometry, like that of a plane, or a “hyper-bolic” geometry, like that of a saddle [see illustration on nextpage]. At first glance, such a universe stretches on forever.

One problem with this conclusion is that the universe couldbe spherical yet so large that the observable part seems Euclid-ean, just as a small patch of the earth’s surface looks flat. Abroader issue, however, is that relativity is a purely local theo-ry. It predicts the curvature of each small volume of space—its


geometry—based on the matter and energyit contains. Neither relativity nor standardcosmological observations say anythingabout how those volumes fit together to givethe universe its overall shape—its topology.The three plausible cosmic geometries areconsistent with many different topologies.For example, relativity would describe botha torus (a doughnutlike shape) and a planewith the same equations, even though thetorus is finite and the plane is infinite.Determining the topology requires somephysical understanding beyond relativity.

The usual assumption is that the uni-verse is, like a plane, “simply connected,”which means there is only one direct pathfor light to travel from a source to an ob-server. A simply connected Euclidean orhyperbolic universe would indeed be infi-nite. But the universe might instead be“multiply connected,” like a torus, inwhich case there would be many differentpaths. An observer would see multiple im-ages of each galaxy and could easily mis-interpret them as distinct galaxies in anendless space, much as a visitor to a mir-rored room has the illusion of seeing a huge crowd.

A multiply connected space is no mere mathematical whim-sy; it is even preferred by some schemes for unifying the funda-mental forces of nature, and it does not contradict any availableevidence. Over the past few years, research into cosmic topolo-gy has blossomed. New observations may soon reach a defini-tive answer.

Comfort in the FiniteMANY COSMOLOGISTS EXPECT the universe to be finite.Part of the reason may be simple comfort: the human mind en-compasses the finite more readily than the infinite. But there arealso two scientific lines of argument that favor finitude. The firstinvolves a thought experiment devised by Isaac Newton and re-visited by George Berkeley and Ernst Mach. Grappling with thecauses of inertia, Newton imagined two buckets partially filledwith water. The first bucket is left still, and the surface of thewater is flat. The second bucket is spun rapidly, and the surfaceof the water is concave. Why?

The naive answer is centrifugal force. But how does the sec-ond bucket know it is spinning? In particular, what defines theinertial reference frame relative to which the second bucketspins and the first does not? Berkeley and Mach’s answer wasthat all the matter in the universe collectively provides the ref-erence frame. The first bucket is at rest relative to distant galax-ies, so its surface remains flat. The second bucket spins rela-tive to those galaxies, so its surface is concave. If there wereno distant galaxies, there would be no reason to prefer one ref-erence frame over the other. The surface in both buckets would

have to remain flat, and therefore the water would require nocentripetal force to keep it rotating. In short, it would have noinertia. Mach inferred that the amount of inertia a body expe-riences is proportional to the total amount of matter in the uni-verse. An infinite universe would cause infinite inertia. Noth-ing could ever move.

In addition to Mach’s argument, there is preliminary workin quantum cosmology, which attempts to describe how the uni-verse emerged spontaneously from the void. Some such theoriespredict that a low-volume universe is more probable than ahigh-volume one. An infinite universe would have zero proba-bility of coming into existence [see “Quantum Cosmology andthe Creation of the Universe,” by Jonathan J. Halliwell; Scien-tific American, December 1991]. Loosely speaking, its ener-gy would be infinite, and no quantum fluctuation could mustersuch a sum.

Historically, the idea of a finite universe ran into its own ob-stacle: the apparent need for an edge. Aristotle argued that theuniverse is finite on the grounds that a boundary was necessaryto fix an absolute reference frame, which was important to hisworldview. But his critics wondered what happened at the edge.Every edge has another side. So why not redefine the “universe”(which roughly means “one side”) to include that other side?German mathematician Georg F. B. Riemann solved the riddlein the mid-19th century. As a model for the cosmos, he pro-posed the hypersphere—the three-dimensional surface of a four-dimensional ball, just as an ordinary sphere is the two-dimen-sional surface of a three-dimensional ball. It was the first ex-ample of a space that is finite yet has no problematic boundary.


Euclidean

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LOCAL GEOMETRY of space can be Euclidean, spherical or hyperbolic—the only possibilitiesconsistent with the observed symmetry of the cosmos on large scales. On the Euclidean plane, the angles of a triangle add to exactly 180 degrees; on the spherical surface, they add to more than 180 degrees; and on the hyperbolic surface (or saddle), to less than 180 degrees. Local geometrydetermines how objects move. But it does not describe how individual volumes connect to give the universe its global shape.


One might still ask what is outside the universe. But thisquestion supposes that the ultimate physical reality must be aEuclidean space of some dimension. That is, it presumes that ifspace is a hypersphere, then that hypersphere must sit in a four-dimensional Euclidean space, allowing us to view it from theoutside. Nature, however, need not cling to this notion. It wouldbe perfectly acceptable for the universe to be a hypersphere andnot be embedded in any higher-dimensional space. Such an ob-ject may be difficult to visualize, because we are used to viewingshapes from the outside. But there need not be an “outside.”

By the end of the 19th century, mathematicians had discov-ered a variety of finite spaces without boundaries. German as-tronomer Karl Schwarzschild brought this work to the atten-tion of his colleagues in 1900. In a postscript to an article inVierteljahrschrift der Astronomischen Gesellschaft, he chal-lenged his readers:

Imagine that as a result of enormously extended astronom-ical experience, the entire universe consists of countless iden-tical copies of our Milky Way, that the infinite space can bepartitioned into cubes each containing an exactly identicalcopy of our Milky Way. Would we really cling on to the as-sumption of infinitely many identical repetitions of the sameworld?. . . We would be much happier with the view thatthese repetitions are illusory, that in reality space has pecu-liar connection properties so that if we leave any one cubethrough a side, then we immediately reenter it through theopposite side.

Schwarzschild’s example illustrates how one can mentallyconstruct a torus from Euclidean space. In two dimensions, be-gin with a square and identify opposite sides as the same—as isdone in many video games, such as the venerable Asteroids, inwhich a spaceship going off the right side of the screen reappearson the left side. Apart from the interconnections between sides,the space is as it was before. All the familiar rules of Euclideangeometry hold. At first glance, the space looks infinite to thosewho live within it, because there is no limit to how far they cansee. Without traveling around the universe and reencounteringthe same objects, the ship could not tell that it is in a torus [seeillustration below]. In three dimensions, one begins with a cu-bical block of space and glues together opposite faces to pro-duce a 3-torus.

The Euclidean 2-torus, apart from some sugar glazing, istopologically equivalent to the surface of a doughnut. Unfor-tunately, the Euclidean torus cannot sit in our three-dimensionalEuclidean space. Doughnuts may do so because they have beenbent into a spherical geometry around the outside and a hyper-bolic geometry around the hole. Without this curvature, dough-nuts could not be viewed from the outside.

When Albert Einstein published the first relativistic modelof the universe in 1917, he chose Riemann’s hypersphere as theoverall shape. At that time, the topology of space was an activetopic of discussion. Russian mathematician Aleksander Fried-mann soon generalized Einstein’s model to permit an expand-ing universe and a hyperbolic space. His equations are still rou-tinely used by cosmologists. He emphasized that the equations

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DOUGHNUT SPACE, more properly known as the Euclidean 2-torus, is a flat square whose oppositesides are connected (1). Anything crossing one edge reenters from the opposite edge. Althoughthis surface cannot exist within our three-dimensional space, a distorted version can be built bytaping together top and bottom (2) and scrunching the resulting cylinder into a ring (3). Forobservers in the pictured red galaxy, space seems infinite because their line of sight never ends(below). Light from the yellow galaxy can reach them along several different paths, so they seemore than one image of it. A Euclidean 3-torus is built from a cube rather than a square.


of his hyperbolic model applied to finite universes as well as tothe standard infinite one—an observation all the more remark-able because, at the time, no examples of finite hyperbolic spaceswere known. In fact, almost all topologies require hyperbolicgeometries. In two dimensions, a finite Euclidean space musthave the topology of either a 2-torus or a Klein bottle; in threedimensions, there are only 10 Euclidean possibilities—namely,the 3-torus and nine simple variations on it, such as gluing to-gether opposite faces with a quarter turn or with a reflection,instead of straight across. By comparison, there are infinitelymany possible topologies for a finite hyperbolic three-dimen-sional universe. Their rich structure is still the subject of intenseresearch. Similarly, there are infinitely many possible topologiesfor a finite spherical three-dimensional universe.

EightfoldOF ALL THE ISSUES in cosmic topology, perhaps the most dif-ficult to grasp is how a hyperbolic space can be finite. For sim-plicity, first consider a two-dimensional universe. Mimic the con-struction of a 2-torus but begin with a hyper-bolic surface instead. Cut out a regular octagonand identify opposite pairs of edges, so thatanything leaving the octagon across one edgereturns at the opposite edge. Alternatively, onecould devise an octagonal Asteroids screen [seeillustration at right]. This is a multiply con-nected universe, topologically equivalent to atwo-holed pretzel. An observer at the center ofthe octagon sees the nearest images of himselfor herself in eight different directions. The illu-sion is that of an infinite hyperbolic space, eventhough this universe is really finite. Similar con-structions are possible in three dimensions, al-though they are harder to visualize.

The angles of the octagon merit carefulconsideration. On a flat surface, a polygon’sangles do not depend on its size. A large regu-lar octagon and a small regular octagon bothhave inside angles of 135 degrees. On a curvedsurface, however, the angles do vary with size.On a sphere the angles increase as the polygongrows, whereas on a hyperbolic surface the an-gles decrease. The above construction requiresan octagon that is just the right size to have 45-degree angles, so that when the opposite sidesare identified, the eight corners will meet at asingle point and the total angle will be 360 de-grees. This subtlety explains why the con-struction would not work with a flat octagon;in Euclidean geometry, eight 135-degree cor-ners cannot meet at a single point. The two-di-mensional universe obtained by identifying op-posite sides of an octagon must be hyperbolic.The topology dictates the geometry.

The size of the polygon or polyhedron is

measured relative to the only geometrically meaningful lengthscale for a space: the radius of curvature. A sphere, for example,can have any physical size (in meters, say), but its surface areawill always be exactly 4π times the square of its radius—thatis, 4π square radians. The same principle applies to the size ofa hyperbolic topology, for which a radius of curvature can alsobe defined. The smallest known hyperbolic space, discovered byone of us (Weeks) in 1985, may be constructed by identifyingpairs of faces of an 18-sided polyhedron. It has a volume of ap-proximately 0.94 cubic radian. Other hyperbolic topologies arebuilt from larger polyhedra.

Just as hyperbolic geometry allows for many topologies, sodoes spherical geometry. In three dimensions, the sphere is gen-eralized into the hypersphere. (To visualize the hypersphere,think of it as being composed of two solid balls in Euclideanspace, glued together along their surface: each point of the sur-face of one ball is the same as the corresponding point on theother ball.) The hypersphere’s volume is exactly 2π2 times thecube of its curvature radius. As early as 1917, Dutch astronomer


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FINITE HYPERBOLIC SPACE is formed by an octagon whose opposite sides are connected, so thatanything crossing one edge reenters from the opposite edge (top left). Topologically, theoctagonal space is equivalent to a two-holed pretzel (top right). Observers on the surface wouldsee an infinite octagonal grid of galaxies. Such a grid can be drawn only on a hyperbolicmanifold, a strange floppy surface where every point has the geometry of a saddle (bottom). SO

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Willem de Sitter distinguished the projective three-sphere (P3)from the ordinary three-sphere, S3. The projective sphere isformed from the sphere by identifying all pairs of antipodalpoints (those directly opposite each other on the sphere). P3

therefore has half the volume of S3. Aside from P3, there are in-finitely many topologies with spherical geometries. Unlike in hy-perbolic geometry—in which the more “complicated” the topol-ogy, the larger the volume of the fundamental polyhedron—inspherical geometry topological complexity leads to ever smallerfundamental polyhedra. For example, the Poincaré space is rep-resented by a dodecahedron whose opposite faces are pairwiseidentified; it has a volume 1⁄120 that of the hypersphere.

Cosmic space may well have such a shape, in which case anextraordinary “spherical lens” would be generated, with imagesof cosmic sources repeating according to the Poincaré space’s120-fold “crystal structure.” From a mathematical point ofview, the volume of the universe, in cubic radians, can be arbi-trarily small even if the curvature of the universe is very large.This means that no matter how close to Euclidean space is ob-served to be, it will always be worth looking for spherical cos-mic topology.

Diverse astronomical observations imply that the density ofmatter in the cosmos is only a third of that needed for space tobe Euclidean. Until recently, it was not known whether a cos-mological constant made up the difference [see “CosmologicalAntigravity,” on page 30] or the universe had a hyperbolicgeometry with a radius of curvature of 18 billion light-years. Yetrecent measurements of the cosmic microwave backgroundstrongly suggest that the geometry is at least quite close to Eu-clidean. Those results, as well as careful measurements of dis-tant supernovae, confirm that something very much like a cos-mological constant is prevalent. Nevertheless, many compacttopologies—Euclidean, hyperbolic and especially spherical—re-main ripe for detection.

The decades from 1930 to 1990 were the dark ages of think-ing on cosmic topology. But the 1990s saw the rebirth of thesubject. Roughly as many papers have been published on cos-

mic topology in the past several years as in the preceding80. Most exciting of all, cosmologists are finally poised todetermine the topology observationally.

The simplest test of topology is to look at the arrange-ment of galaxies. If they lie in a rectangular lattice, with im-ages of the same galaxy repeating at equivalent latticepoints, the universe is a 3-torus. Other patterns reveal morecomplicated topologies. Unfortunately, looking for suchpatterns can be difficult, because the images of a galaxywould depict different points in its history. Astronomerswould need to recognize the same galaxy despite changesin appearance or shifts in position relative to neighboringgalaxies. Over the past quarter of a century researcherssuch as Dmitri Sokoloff of Moscow State University, Vik-tor Shvartsman of the Soviet Academy of Sciences inMoscow, J. Richard Gott III of Princeton University andHelio V. Fagundes of the Institute for Theoretical Physicsin São Paulo have looked for and found no repeating im-

ages within one billion light-years of the earth.Others—such as Boudewijn F. Roukema, now at the Center

of Astronomy of the Nicolaus Copernicus University in Torun,Poland—have sought patterns among quasars. Because theseobjects, thought to be powered by black holes, are bright, anypatterns among them can be seen from large distances. The ob-servers identified all groupings of four or more quasars. By ex-amining the spatial relations within each group, they checkedwhether any pair of groups could in fact be the same group seenfrom two different directions. Roukema identified two possi-bilities, but they may not be statistically significant.

Roland Lehoucq and Marc Lachièze-Rey of the departmentof astrophysics at CEA Saclay in France, together with Jean-Philippe Uzan of the Theoretical Physics Laboratory in Orsayand one of us (Luminet), have circumvented the problems ofgalaxy recognition in the following way. We have developedvarious methods of cosmic crystallography that can make out apattern statistically without needing to recognize specific galax-ies as images of one another. If galaxy images repeat periodi-cally, a histogram of all galaxy-to-galaxy distances should showpeaks at certain distances, which reflect the true size of the uni-verse. The method has been shown to work well theoretically ina Euclidean or spherical universe. So far we have seen no pat-


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DISTANCES BETWEEN GALAXY CLUSTERS do not show the pattern expected for a finite, interconnected universe—namely, sharp peaks at distances related tothe true size of the cosmos (inset). But we (the authors) only studied clusterswithin roughly two billion light-years of the earth. The universe could still beinterconnected on larger scales.

JEAN-PIERRE LUMINET, GLENN D. STARKMAN and JEFFREY R.WEEKS say they relish participating in the boom years of cosmictopology, as researchers come together across disciplinaryboundaries. Luminet, who studies black holes and cosmology atParis Observatory, has written several books of science as well aspoetry and has collaborated with composer Gérard Grisey on themusical performance Le Noir de l’étoile. Starkman was institu-tionalized for six years—at the Institute for Advanced Study inPrinceton, N.J., and then at the Canadian Institute for TheoreticalAstrophysics in Toronto. He has been released into the custody ofCase Western Reserve University. Weeks, the mathematician ofthe trio, was named a MacArthur Fellow in 1999 and is currentlyan independent scholar.

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tern [see illustration on preceding page], but this may be becauseof the paucity of real data on galaxies farther away than two bil-lion light-years. The Sloan Digital Sky Survey—an ongoingAmerican-Japanese collaboration to prepare a three-dimen-sional map of much of the universe—and other high-redshiftgalaxy surveys in progress will produce a larger data set for thesestudies.

Finally, several other research groups plan to ascertain thetopology of the universe using the cosmic microwave back-ground, the faint glow remaining from the big bang. The radi-ation is remarkably homogeneous: its temperature and intensi-ty are the same in all parts of the sky to nearly one part in100,000. But there are slight undulations discovered in 1991 bythe Cosmic Background Explorer (COBE) satellite. Roughlyspeaking, the microwave background depicts density variationsin the early universe, which ultimately seeded the growth of starsand galaxies.

Circular ReasoningTHESE FLUCTUATIONS are the key to resolving a variety ofcosmological issues, and topology is one of them. Microwavephotons arriving at any given moment began their journeys atapproximately the same time and distance from the earth. Sotheir starting points form a sphere,called the last scattering surface, withthe earth at the center. Just as a suffi-ciently large paper disk overlaps itselfwhen wrapped around a broom han-dle, the last scattering surface will in-tersect itself if it is big enough to wrapall the way around the universe. Theintersection of a sphere with itself issimply a circle of points in space.

Looking at that circle from theearth, astronomers would see two cir-cles in the sky that share the same pat-tern of temperature variations. Thosetwo circles are really the same circle inspace seen from two perspectives [seeillustration at right]. They are analogousto the multiple images of a candle in amirrored room, each of which showsthe candle from a different angle.

Two of us (Starkman and Weeks),working with David N. Spergel ofPrinceton and Neil J. Cornish of Mon-tana State University, hope to detect

such circle pairs. The beauty of this method is that it is unaf-fected by the uncertainties of contemporary cosmology—it re-lies on the observation that space has constant curvature, but itmakes no assumptions about the density of matter, the geome-try of space or the presence of a cosmological constant. Themain problem is to identify the circles despite the forces that tendto distort their images. For example, as galaxies coalesce, theyexert a varying gravitational pull on the radiation as it travelstoward the earth, shifting its energy.

Unfortunately, COBE was incapable of resolving structureson an angular scale of less than 10 degrees. Moreover, it did notidentify individual hot or cold spots; all one could say for sureis that statistically some of the fluctuations were real featuresrather than instrumental artifacts. Higher-resolution and low-er-noise instruments have since been developed. Some are al-ready making observations from ground-based or balloon-borne observatories, but they do not cover the whole sky. Thecrucial observations will be made by NASA’s Microwave An-isotropy Probe (MAP), now gathering data, and the EuropeanSpace Agency’s Planck satellite, scheduled for launch in 2007.

The relative positions of the matching circles, if any, will re-veal the specific topology of the universe. If the last scatteringsurface is barely big enough to wrap around the universe, it will

EarthEarth

WRAPPED AROUND THE COSMOS, light creates patterns in the sky.All the light received from a specific time or from a specificdistance from the earth—such as the cosmic microwavebackground radiation left over from the big bang—represents asphere. If this sphere is larger than the universe, it will intersectitself, defining a circle. This circle consists of those points we seetwice: from the left and from the right (right). A two-dimensionalanalogy is a circular bandage wrapped around a finger (above).

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64 S C I E N T I F I C A M E R I C A N T H E O N C E A N D F U T U R E C O S M O SCOPYRIGHT 2002 SCIENTIFIC AMERICAN, INC.

intersect only its nearest ghost images. If it is larger, it will reachfarther and intersect the next nearest images. If the last scatter-ing surface is large enough, we expect hundreds or even thou-sands of circle pairs [see illustration above]. The data will behighly redundant. The largest circles will completely determinethe topology of space as well as the position and orientation ofall smaller circle pairs. Thus, the internal consistency of the pat-terns will verify not just the correctness of the topological find-ings but also the correctness of the microwave background data.

Other teams have different plans for the data. John D. Bar-row and Janna J. Levin of the University of Cambridge, EmoryF. Bunn of St. Cloud State University, Evan Scannapieco of theAstrophysical Observatory of Arcetri, Italy, and Joseph I. Silkof the University of Oxford intend to examine the pattern of hotand cold spots directly. The group has already constructed sam-ple maps simulating the microwave background for particulartopologies. They have multiplied the temperature in each di-rection by the temperature in every other direction, generatinga huge four-dimensional map of what is usually called the two-point correlation function. The maps provide a quantitative wayof comparing topologies. J. Richard Bond of the Canadian In-stitute for Theoretical Astrophysics in Toronto, Dmitry Pogo-syan of the University of Alberta and Tarun Souradeep of theInter-University Center for Astronomy and Astrophysics inPune, India, were among the first to apply related new tech-niques to the existing COBE data, which could accurately iden-tify the smallest hyperbolic spaces.

Beyond the immediate intellectual satisfaction, discoveringthe topology of space would have profound implications forphysics. Although relativity says nothing about the universe’stopology, newer and more comprehensive theories that are un-der development should predict the topology or at least assignprobabilities to the various possibilities. These theories are need-ed to explain gravity in the earliest moments of the big bang,when quantum-mechanical effects were important [see “Quan-tum Gravity,” by Bryce S. DeWitt; Scientific American, De-cember 1983]. The theories of everything, such as M-theory, are

in their infancy and do not yet have testable consequences. Buteventually the candidate theories will make predictions aboutthe topology of the universe on large scales.

The tentative steps toward the unification of physics have al-ready spawned the subfield of quantum cosmology. There arethree basic hypotheses for the birth of the universe, which areadvocated, respectively, by Andrei Linde of Stanford Universi-ty, Alexander Vilenkin of Tufts University and Stephen W.Hawking of the University of Cambridge. One salient point ofdifference is whether the expected volume of a newborn uni-verse is very small (Linde’s and Vilenkin’s proposals) or verylarge (Hawking’s). Topological data may be able to distinguishamong these models.

Since ancient times, cultures around the world have askedhow the universe began and whether it is finite or infinite.Through a combination of mathematical insight and careful ob-servation, science in the 20th century partially answered the firstquestion. It might begin the 21st century with an answer to thesecond as well.


La Biblioteca de Babel (The Library of Babel). Jorge Luis Borges inFicciones. Emecé Editores, 1956. Text available atjubal.westnet.com/hyperdiscordia/library__of__babel.html

Cosmic Topology. Marc Lachièze-Rey and Jean-Pierre Luminet in PhysicsReports, Vol. 254, No. 3, pages 135–214; March 1995. Preprint availableat xxx.lanl.gov/abs/gr-qc/9605010

Circles in the Sky: Finding Topology with the Microwave BackgroundRadiation. Neil J. Cornish, David N. Spergel and Glenn D. Starkman inClassical and Quantum Gravity, Vol. 15, No. 9, pages 2657–2670;September 1998. Preprint available at xxx.lanl.gov/abs/astro-ph/9801212

Reconstructing the Global Topology of the Universe from the CosmicMicrowave Background. Jeffrey R. Weeks in Classical and QuantumGravity, Vol. 15, No. 9, pages 2599–2604; September 1998. Preprintavailable at xxx.lanl.gov/abs/astro-ph/9802012

Free software for exploring topology is available atwww.northnet.org/weeks

L’Univers chiffonné. Jean-Pierre Luminet. Fayard, Paris, 2001.

The Shape of Space. Jeffrey R. Weeks. Marcel Dekker, Paris, 2002.


THREE POSSIBLE UNIVERSES, large, medium and small (top row), would produce distinctive patterns in the cosmic microwavebackground radiation, as simulated here (bottom row). Each of these universes has the topology of a 3-torus and is shown repeatedsix times to evoke the regular grid that an observer would see. In the large universe, the sphere of background radiation does notoverlap itself, so no patterns emerge. In the medium universe, the sphere intersects itself once in each direction. One may verifythat tracing clockwise around the central circle in the left hemisphere reveals the same sequence of colors as tracing counter-clockwise in the right. Finally, in the small universe, the sphere intersects itself many times, resulting in a more complex pattern.

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66 S C I E N T I F I C A M E R I C A N U p d a t e d f r o m t h e A u g u s t 2 0 0 0 i s s u e

THE CLASSIC 1884 story Flatland: A Romance ofMany Dimensions, by Edwin A. Abbott, describesthe adventures of “A. Square,” a character wholives in a two-dimensional world populated by an-imated geometric figures—triangles, squares, pen-tagons and so on. Toward the end of the story, on

the first day of 2000, a spherical creature from three-dimen-sional “Spaceland” passes through Flatland and carries A.Square up off his planar domain to show him the true three-dimensional nature of the larger world. As he comes to graspwhat the sphere is showing him, A. Square speculates thatSpaceland may itself exist as a small subspace of a still largerfour-dimensional universe.

Amazingly, in the past four years physicists have begun se-riously examining a very similar idea: that everything we cansee in our universe is confined to a three-dimensional “mem-brane” that lies within a higher-dimensional realm. But unlikeA. Square, who had to rely on divine intervention from Space-land for his insights, physicists may soon be able to detect andverify the existence of reality’s extra dimensions, which couldextend over distances as large as a millimeter. Experiments arealready looking for the extra dimensions’ effect on the forceof gravity. If the theory is correct, upcoming high-energy par-ticle experiments in Europe could see unusual processes in-volving quantum gravity, such as the creation of transitory mi-cro black holes. More than just an idle romance of many di-mensions, the theory is based on some of the most recent

developments in string theory and would solve some long-standing puzzles of particle physics and cosmology.

The exotic concepts of string theory and multidimensionsactually arise from attempts to understand the most familiar offorces: gravity. More than three centuries after Isaac Newtonproposed his law of gravitation, physics still does not explainwhy gravity is so much weaker than all the other forces. Thefeebleness of gravity is dramatic. A small magnet readily over-comes the gravitational pull of the entire mass of the earthwhen it lifts a nail off the ground. The gravitational attractionbetween two electrons is 1043 times weaker than the repulsiveelectric force between them. Gravity seems important to us—

keeping our feet on the ground and the earth orbiting the sun—

only because these large aggregates of matter are electricallyneutral, making the electrical forces vanishingly small and leav-ing gravity, weak as it is, as the only noticeable force left over.

The Inexplicable Weakness of GravityELECTRONS WOULD HAVE to be 1022 times more massivefor the electric and gravitational forces between two of them tobe equal. To produce such a heavy particle would take 1019 giga-electron volts (GeV) of energy, a quantity known as the Planckenergy (after German physicist Max Planck). A related quan-tity is the Planck length, a tiny 10–35 meter. By comparison, thenucleus of a hydrogen atom, a proton, is about 1019 times aslarge and has a mass of about 1 GeV. The Planck scale of en-ergy and length is far out of reach of the most powerful accel-

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erators. Even the Large Hadron Collider at CERN will probedistances only down to about 10–19 meter when it commencesoperations five years from now [see “The Large Hadron Col-lider,” by Chris Llewellyn Smith; Scientific American, July2000]. Because gravity becomes comparable in strength to elec-tromagnetism and the other forces at the Planck scale, physi-cists have traditionally assumed that the theory unifying grav-ity with the other interactions would reveal itself only at theseenergies. The nature of the ultimate unified theory would thenbe hopelessly out of reach of direct experimental investigationin the foreseeable future [see “A Unified Physics by 2050?” bySteven Weinberg; Scientific American, December 1999].

Today’s most powerful accelerators probe the energy realmbetween 100 and 1,000 GeV (one teraelectron volt, or TeV).In this range, experimenters have seen the electromagnetic forceand the weak interaction (a force between subatomic particlesresponsible for certain types of radioactive decay) become uni-fied. We would understand gravity’s extraordinary weaknessif we understood the factor of 1016 that separates the elec-troweak scale from the Planck scale.

Alas, physicists’ extremely successful theory of particlephysics, called the Standard Model, cannot explain the size ofthis huge gap, because the theory is carefully adjusted to fit theobserved electroweak scale. The good news is that this adjust-ment (along with about 16 others) serves once and for all tofit myriad observations. The bad news is that we must fine-tune

the underlyingtheory to an accu-racy of about one partin 1032; otherwise, quantumeffects—instabilities—would dragthe electroweak scale all the way backup to the Planck scale. The presence of suchdelicate balancing in the theory is like walking into a room andfinding a pencil standing perfectly on its tip in the middle of atable. Though not impossible, the situation is highly unstable,and we are left wondering how it came about.

For 20 years, theorists have attacked this conundrum,called the hierarchy problem, by altering the nature of particlephysics near 10–19 meter (or 1 TeV) to stabilize the electroweakscale. The most popular modification of the Standard Modelthat achieves this goal involves a new symmetry called super-symmetry. Going back to our pencil analogy, supersymmetryacts like an invisible thread holding up the pencil and prevent-ing it from falling over. Although accelerators have not yetturned up any direct evidence for supersymmetry, some sug-gestive indirect evidence supports the theory. For example,when the measured strengths of the strong, weak and electro-magnetic forces are theoretically extrapolated to shorter dis-tances, they meet very accurately at a common value only if su-persymmetric rules govern the extrapolation. This result hintsat a supersymmetric unification of these three forces at about


MEMBRANE UNIVERSE in a higher-dimensional realm could bewhere we live. Experiments might detect signs of extra dimensionsclose to a millimeter in size in the near future.


10–32 meter, approximately 1,000 times larger than the Plancklength but still far beyond the range of particle colliders.

Gravity and Large Spatial DimensionsFOR TWO DECADES, the only viable framework for tacklingthe hierarchy problem has been to change particle physics near10–19 meter by introducing new processes such as supersym-metry. But in the past four years, theorists have proposed a rad-ically different approach, modifying spacetime, gravity and thePlanck scale itself. The key insight is that the extraordinary sizeof the Planck scale, accepted for a century since Planck first in-troduced it, is based on an untested assumption about how grav-ity behaves over short distances.

Newton’s inverse square law of gravity—which says theforce between two masses falls as the square of the distance be-tween them—works extremely well over macroscopic distances,explaining the earth’s orbit around the sun, and so on. But be-cause gravity is so weak, the law has been experimentally test-ed down to distances of only about a millimeter, and we mustextrapolate across 32 orders of magnitude to conclude that

gravity becomes strong only at a Planck scale of 10–35 meter.The inverse square law is natural in three-dimensional space

[see upper illustration on opposite page]. Consider lines of grav-itational force emanating uniformly from the earth. Farther fromthe earth, the lines are spread over a spherical shell of greaterarea. The surface area increases as the square of the distance, andso the force is diluted at that rate. Suppose there were one moredimension, making space four-dimensional. Then the field linesemanating from a point would get spread over a four-dimen-sional shell whose surface would increase as the cube of the dis-tance, and gravity would follow an inverse cube law.

The inverse cube law certainly doesn’t describe our universe,but now imagine that the extra dimension is curled up into asmall circle of radius R and that we’re looking at field lines com-ing from a tiny point mass [see lower illustration on oppositepage]. When the field lines are much closer to the mass than thedistance R, they can spread uniformly in all four dimensions,and so the force of gravity falls as the inverse cube of distance.Once the lines have spread fully around the circle, however, onlythree dimensions remain for them to continue spreading

IN A NUTSHELL by Graham P. Collins

DIMENSIONS. Our universe seems to have four dimensions:three of space (up-down, left-right, forward-backward) and oneof time. Although we can barely imagine additional dimensions,mathematicians and physicists have long analyzed theproperties of theoretical spaces that have any number.

SIZE OF DIMENSIONS. The four known spacetime dimensions ofour universe are vast. The dimension of time extends back atleast 13 billion years into the past and may extend infinitelyinto the future. The three spatial dimensions may be infinite; our telescopes have detected objects more than 12 billion light-years away. Dimensions can also be finite. For example,the two dimensions of the surface of the earth extend onlyabout 40,000 kilometers—the length of a great circle.

SMALL EXTRA DIMENSIONS. Some modern physics theoriespostulate additional real dimensions that are wrapped up incircles so small (perhaps 10–35-meter radius) that we have notdetected them. Think of a thread of cotton: to a goodapproximation, it is one-dimensional. A single number canspecify where an ant stands on the thread. But using amicroscope, we see dust mites crawling on the thread’s two-dimensional surface: along the large length dimension andaround the short circumference dimension.

LARGE EXTRA DIMENSIONS. Recently physicists realized thatextra dimensions as big as a millimeter could exist and remaininvisible to us. Surprisingly, no known experimental data rule outthe theory, and it could explain several mysteries of particle

physics and cosmology. We and all the contentsof our known three-dimensional universe (except

for gravity) would be stuck on a membrane, like ballsmoving on the two-dimensional green baize of a pool table.

DIMENSIONS AND GRAVITY. The behavior of gravity—

particularly its strength—is intimately related to how manydimensions it pervades. Studies of gravity acting overdistances smaller than a millimeter could thus reveal largeextra dimensions to us. Such experiments are under way.These dimensions would also enhance the production ofbizarre quantum gravity objects such as micro black holes,graviton particles and superstrings, all of which could bedetected sometime this decade at high-energy particleaccelerators.

Graham P. Collins is a staff editor and writer.


BALLS ON A POOL TABLE are analogous tofundamental particles on the membrane that is our known universe. Billiard ball collisions radiateenergy into three dimensions as sound waves (red),analogous to gravitons. Precise studies of the balls’ motions coulddetect the missing energy and thus the higher dimensions.

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through, and so for distances much greater than R the forcevaries as the inverse square of the distance.

The same effect occurs if there are many extra dimensions,all curled up into circles of radius R. For n extra spatial dimen-sions at distances smaller than R, the force of gravity will fol-low an inverse 2 + n power law. Because we have measuredgravity only down to about a millimeter, we would be obliviousto changes in gravity caused by extra dimensions for which Rwas smaller than a millimeter. Furthermore, the 2 + n power lawwould cause gravity to reach Planck-scale strength well above10–35 meter. That is, the Planck length (defined by where grav-ity becomes strong) would not be that small, and the hierarchyproblem would be reduced.

One can solve the hierarchy problem completely by postu-lating enough extra dimensions to move the Planck scale veryclose to the electroweak scale. The ultimate unification of grav-ity with the other forces would then take place near 10–19 me-ter rather than 10–35 meter as traditionally assumed. How manydimensions are needed depends on how large they are. Con-versely, for a given number of extra dimensions we can computehow large they must be to make gravity strong near 10–19 me-ter. If there is only one extra dimension, its radius R must beroughly the distance between the earth and the sun. Therefore,this case is already excluded by observation. Two extra dimen-sions, however, can solve the hierarchy problem if they areabout a millimeter in size—precisely where our direct knowl-edge of gravity ends. The dimensions are smaller still if we addmore of them, and for seven extra dimensions we need them tobe around 10–14 meter big, about the size of a uranium nucleus.This is tiny by everyday standards but huge by the yardstick ofparticle physics.

Postulating extra dimensions may seem bizarre and ad hoc,but to physicists it is an old, familiar idea that dates back to the1920s, when Polish mathematician Theodor Kaluza and Swed-ish physicist Oskar Klein developed a remarkable unified theo-ry of gravity and electromagnetism that required one extra di-mension. The idea has been revived in modern string theories,which require a total of 10 spatial dimensions for internal math-ematical consistency. In the past, physicists have assumed thatthe extra dimensions are curled up into tiny circles with a size

near the traditional Planck length of 10–35 meter, making themundetectable but also leaving the conundrum of the hierarchyproblem. In contrast, in the new theory that we are discussing,the extra dimensions are wrapped into big circles of at least 10–14

meter radius and perhaps as enormous as a millimeter.

Our Universe on a WallIF THESE DIMENSIONS are that large, why haven’t we seenthem yet? Extra dimensions a millimeter big would be dis-cernible to the naked eye and obvious through a microscope.And although we have not measured gravity much below abouta millimeter, we have a wealth of experimental knowledge con-cerning all the other forces at far shorter distances, approaching10–19 meter, all of it consistent only with three-dimensionalspace. How could there possibly be large extra dimensions?

The answer is at once simple and peculiar: all the matter andforces we know of—with the sole exception of gravity—arestuck to a “wall” in the space of the extra dimensions [see il-lustration on next page]. Electrons, protons, photons and all theother particles in the Standard Model cannot move in the extra


SMALL EXTRA DIMENSION wrapped in a circle (circumference of tube)modifies how gravity (red lines) spreads in space. At distances smallerthan the circle radius (blue patch), the lines of force spread apart

rapidly through all the dimensions. At much larger distances (yellowcircle), the lines have filled the extra dimension, which has no furthereffect on the lines of force.

GRAVITATIONAL LINES OF FORCE spread out from the earth in threedimensions. As distance from the earth increases, the force becomesdiluted by being spread across a larger surface area (spheres). The surfacearea of each sphere increases as the square of its radius, so gravity falls as the inverse square of distance in three dimensions.

Lines of force


dimensions; electric and magnetic field lines cannot spread intothe higher-dimensional space. The wall has only three dimen-sions, and as far as these particles are concerned, the universemight as well be three-dimensional. Only gravitational field linescan extend into the higher-dimensional space, and only the par-ticle that transmits gravity, the graviton, can travel freely intothe extra dimensions. The presence of the extra dimensions canbe felt only through gravity.

To make an analogy, imagine that all the particles in theStandard Model, like electrons and protons, are billiard ballsmoving on the surface of a vast pool table. As far as they areconcerned, the universe is two-dimensional. Nevertheless,pool-table inhabitants made out of billiard balls could still de-tect the higher-dimensional world: when two balls hit each oth-er sufficiently hard, they produce sound waves, which travel inall three dimensions, carrying some energy away from the tablesurface [see illustration on page 68]. The sound waves are anal-ogous to gravitons, which can travel in the full higher-dimen-sional space. In high-energy particle collisions, we expect to ob-serve missing energy, the result of gravitons escaping into theextra dimensions.

Although it may seem strange that some particles should beconfined to a wall, similar phenomena are quite familiar. For in-stance, electrons in a copper wire can move only along the one-dimensional space of the wire and do not travel into the sur-rounding three-dimensional space. Likewise, water waves trav-el primarily on the surface of the ocean, not throughout its depth.The specific scenario we are describing, in which all particles ex-cept gravity are stuck to a wall, can arise naturally in string the-ory. In fact, one of the major insights triggering recent break-throughs in string theory has been the recognition that the the-ory contains such walls, known as D-branes (“brane” comesfrom the word “membrane,” and “D” stands for “Dirichlet,”which indicates a mathematical property of the branes). D-braneshave precisely the required features: particles such as electronsand photons are represented by tiny lengths of string that eachhave two end points that must be stuck to a D-brane. Gravitons,

on the other hand, are tiny closed loops of string that can wan-der into all the dimensions because they have no end points an-choring them to a D-brane.

Is It Alive?ONE OF THE FIRST THINGS good theorists do when theyhave a new theory is to try to kill it by finding an inconsisten-cy with experimental results. The theory of large extra dimen-sions changes gravity at macroscopic distances and alters oth-er physics at high energies, so surely it is easy to kill. Remark-ably, however, it does not contradict any known experiment.A few examples show how surprising this conclusion is.

One might initially worry that changing gravity would af-fect objects held together by gravity, such as stars and galaxies.But they are not affected. Gravity changes only at distancesshorter than a millimeter, whereas in a star, for example, grav-ity acts across thousands of kilometers to hold distant parts ofthe star together.

A much more serious concern relates to gravitons, the hy-pothetical particles that transmit gravity in a quantum theory.In the theory with extra dimensions, gravitons interact muchmore strongly with matter, so many more of them should beproduced in high-energy particle collisions. In addition, theypropagate in all the dimensions, thus taking energy away fromthe wall, or membrane, that is the universe where we live.

When a star collapses and explodes as a supernova, the hightemperatures can readily boil off gravitons into extra dimen-


OUR UNIVERSE MAY EXIST ON A WALL, or membrane, in theextra dimensions. The line along the cylinder (below, right) and theflat plane represent our three-dimensional universe, to which all the knownparticles and forces except gravity are stuck. Gravity (red lines)propagates through all the dimensions. The extra dimensions may be aslarge as one millimeter without violating any existing observations.

GravityOur 3-D universe

Gravity

Extra dimensions


sions [see upper illustration on next page]. From observationsof the famous supernova 1987A, however, we know that theexplosion emits most of its energy as neutrinos, leaving littleroom for any energy leakage by gravitons. Our understandingof supernovae therefore limits how strongly gravitons can cou-ple to matter. This constraint could easily have killed the ideaof large extra dimensions, but detailed calculations show thatthe theory survives. The most severe limit is for only two extradimensions, in which case gravitons cool supernovae too much.

Theorists have examined many other possible constraintsbased on unacceptable changes. The theory passes all these ex-perimental checks, which turn out to be less stringent than thesupernova constraint. Perhaps surprisingly, the constraints be-come less severe as more dimensions are added to the theory.We saw this right from the start: the case of one extra dimen-sion was excluded immediately because gravity would be alteredat solar system distances. This indicates why more dimensionsare safer: the dramatic strengthening of gravity begins at short-er distances and therefore has a smaller impact on the larger-distance processes.

Answers by 2010THE THEORY SOLVES the hierarchy problem by makinggravity a strong force near TeV energies, precisely the energyscale to be probed using upcoming particle accelerators. Ex-periments at the Large Hadron Collider (LHC), due to beginaround 2007, should therefore uncover the nature of quantumgravity! For instance, if string theory is the correct descriptionof quantum gravity, particles are like tiny loops of string thatcan vibrate like a violin string. The known fundamental parti-cles correspond to a string that is not vibrating, much like an un-bowed violin string. Each different “musical note” that a stringcan carry by vibrating would appear as a different, exotic newparticle. In conventional string theories, the strings have beenthought of as only 10–35 meter long, and the new particles wouldhave masses on the order of the traditional Planck energy—the“music” of such strings would be too high-pitched for us to

“hear” at particle colliders. But with large extra dimensions, thestrings are much longer, near 10–19 meter, and the new particleswould appear at TeV energies—low enough to hear at the LHC.

Similarly, the energies needed to create micro black holesin particle collisions would fall within experimental range [seelower illustration on next page].

Even at energies too low to produce vibrating strings orblack holes, particle collisions would produce large numbersof gravitons, a process that is negligible in conventional theo-ries. The experiments could not directly detect the emitted gravi-tons, but the energy they carry off would show up as energymissing from the collision debris. The theory predicts specificproperties of the missing energy—how it should vary with col-lision energy and so on—so evidence of graviton production canbe distinguished from other processes that can carry off energyin unseen particles. Current data from the highest-energy ac-celerators already mildly constrain the large-dimensions sce-nario. Experiments at the LHC should either see evidence ofgravitons or begin to exclude the theory by their absence.

A completely different type of experiment could also sub-stantiate the theory, perhaps much sooner than the particle col-liders. Recall that for two extra dimensions to solve the hierar-chy problem, they must be as large as a millimeter. Measure-ments of gravity would then detect a change from Newton’sinverse square law to an inverse fourth power law at distancesnear a millimeter. Extensions of the basic theoretical frameworklead to a whole host of other possible deviations from New-tonian gravity, the most interesting of which is repulsive forcesmore than a million times stronger than gravity occurring be-tween masses separated by less than a millimeter. Tabletop ex-periments using exquisitely built detectors are now under way,testing Newton’s law from the centimeter range down to tensof microns [see illustration on page 73].

To probe the gravitational force at submillimeter distances,one must use objects not much larger than a millimeter, whichtherefore have very small masses. One must carefully screen outnumerous effects, such as residual electrostatic forces, that could


PARALLEL UNIVERSES may exist invisibly alongside ours, on their ownmembranes less than a millimeter away from ours. Such parallel universescould also be different sheets of our own universe folded back on itself. So-called dark matter could be explained by ordinary stars and galaxies on

nearby sheets: their gravity (red) can reach us by taking a shortcutthrough the extra dimensions, but we cannot see them because light(yellow) must travel billions of light-years to the folds and back before itreaches the earth.

Gravity

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mask or fake the tiny gravitational attraction. Such experimentsare difficult and subtle, but it is exciting that they might uncov-er dramatic new physics. Even apart from the search for extradimensions, it is important to extend our direct knowledge ofgravity to these short distances. Researchers at the Universityof Washington have performed a measurement of gravity downto one fifth of a millimeter and have found no deviations fromNewtonian gravity. Therefore, any large new dimensions mustbe less than a fifth of a millimeter in size. Several groups arenow looking to improve on this measurement.

The idea of extra dimensions in effect continues the Coper-nican tradition in understanding our place in the world: Theearth is not the center of the solar system, the sun is not the cen-ter of our galaxy, our galaxy is just one of billions in a universethat has no center, and now our entire three-dimensional uni-verse would be just a thin membrane in the full space of di-mensions. If we consider slices across the extra dimensions, ouruniverse would occupy a single infinitesimal point in each slice,surrounded by a void.

Perhaps this is not the full story. Just as the Milky Way is notthe only galaxy in the universe, might our universe not be alonein the extra dimensions? The membranes of other three-dimen-sional universes could lie parallel to our own, only a millimeterremoved from us in the extra dimensions [see illustration on pre-ceding page]. Similarly, although all the particles of the Stan-

dard Model must stick to our own membrane universe, otherparticles beyond the Standard Model might propagate throughthe extra dimensions. Far from being empty, the extra dimen-sions could have a multitude of interesting structures.

The effects of new particles and universes in the extra di-mensions may provide answers to many outstanding mysteriesof particle physics and cosmology. For example, they may ac-count for the masses of the ghostly elementary particles calledneutrinos. Impressive evidence from the Super Kamiokande ex-periment in Japan indicates that neutrinos, long assumed to bemassless, have a minuscule but nonzero mass. The neutrino cangain its mass by interacting with a partner field living in the ex-tra dimensions. As with gravity, the interaction is greatly dilut-ed by the partner’s being spread throughout the extra dimen-sions, and so the neutrino acquires only a tiny mass.

Parallel UniversesANOTHER EXAMPLE is the mystery in cosmology of whatconstitutes dark matter, the invisible gravitating substance thatseems to make up more than 90 percent of the mass of the uni-verse. Dark matter may reside in parallel universes. Such mat-ter would affect our universe through gravity and is necessarily“dark” because our species of photon is stuck to our membrane,so photons cannot travel across the void from the parallel mat-ter to our eyes.

Such parallel universes might be utterly unlike our own, hav-ing different particles and forces and perhaps even being con-fined to membranes with fewer or more dimensions. In one in-triguing scenario, however, they have identical properties to ourown world. Imagine that the wall where we live is folded a num-ber of times in the extra dimensions [see illustration on preced-ing page]. Objects on the other side of a fold will appear to bevery distant even if they are less than a millimeter from us inthe extra dimensions: the light they emit must travel to the creaseand back to reach us. If the crease is tens of billions of light-yearsaway, no light from the other side could have reached us sincethe universe began.


SUPERNOVA occurs when the collapse of a massive star produces anexplosive shock wave. Most of the energy is emitted as neutrinos (blue). If extra dimensions exist, radiated gravitons (red) carry away more energythan they would in three dimensions. Theorists constrain the properties of the extra dimensions by requiring that energy leakage by gravitons notcause supernovae to fizzle.

MICRO BLACK HOLES could be created in particle accelerators such as the Large Hadron Collider by smashing together protons (yellow) at highenergies. The holes would evaporate rapidly by emitting Hawking radiationof Standard Model particles (blue) and gravitons (red).

Gravitons

Neutrinos

Supernovacollapse

GravitonsMicro black hole

Our universe

Our universe

Proton Particles

NIMA ARKANI-HAMED, SAVAS DIMOPOULOS and GEORGI DVALI con-ceived the extra-dimension theory at Stanford University in Febru-ary 1998. Arkani-Hamed was born in Houston and in 1997 receiveda Ph.D. in physics at the University of California, Berkeley, where hehas been assistant professor since 1999. When he’s not exploringtheoretical possibilities beyond the Standard Model of particlephysics, he enjoys hiking in the High Sierra and the California desert.Dimopoulos grew up in Athens, received a Ph.D. from the Universityof Chicago and has been professor of physics at Stanford since1979. His research has mostly been driven by the quest for whatlies beyond the Standard Model. In 1981, together with HowardGeorgi of Harvard University, he proposed the supersymmetric Stan-dard Model. “Gia” Dvali was raised in what is now the Republic ofGeorgia and in 1992 received his Ph.D. in high-energy physics andcosmology from Tbilisi State University. In 1998 he became asso-ciate professor of physics at New York University. He enjoys over-coming gravity by high mountaineering and rock and ice climbing.

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Dark matter could be composed of ordinary matter, perhapseven ordinary stars and galaxies, shining brightly on their ownfolds. Such stars would produce interesting observable effects,such as gravitational waves from supernovae. Gravitational-wavedetectors scheduled for completion soon could find evidence forfolds by observing large sources of gravitational radiation thatcannot be accounted for by matter visible in our own universe.

Our theory is not the first proposal involving extra dimen-sions larger than 10–35 meter. In 1990 Ignatios Antoniadis ofthe École Polytechnique in France suggested that some of stringtheory’s dimensions might be as large as 10–19 meter. In 1996Petr Horava of the California Institute of Technology and Ed-ward Witten of the Institute for Advanced Study in Princeton,N.J., pointed out that a single extra dimension of 10–30 meterwould neatly unify forces. Following this idea, Joseph Lykkenof Fermi National Accelerator Laboratory in Batavia, Ill., at-tempted to lower the unification scale to near 10–19 meter.Keith Dienes of the University of Arizona, Emilian Dudas of theUniversity of Paris–South and Tony Gherghetta, now at the Uni-versity of Minnesota, observed in 1998 that extra dimensionssmaller than 10–19 meter could allow the forces to unify at dis-tances much larger than 10–32 meter.

Since our proposal in 1998 a number of interesting varia-tions have appeared, using the same basic ingredients of extradimensions and our universe-on-a-wall. In an intriguing mod-el, Lisa Randall of Harvard University and Raman Sundrum ofJohns Hopkins University proposed that gravity itself may beconcentrated on a membrane in a five-dimensional spacetimethat is infinite in all directions. Gravity appears very weak in our

universe in a natural way if we are on a different membrane.For 20 years, the conventional approach to tackling the hier-

archy problem, and therefore understanding why gravity is soweak, had been to assume that the Planck scale near 10–35 me-ter is fundamental and that particle physics must change near10–19 meter. Quantum gravity would remain in the realm ofspeculation, hopelessly out of the reach of experiment. We nowrealize this does not have to be the case. If there are large newdimensions, in the next several years we could discover devia-tions from Newton’s law near 6 × 10–5 meter, say, and wewould detect stringy vibrations or black holes at the LHC.Quantum gravity and string theory would become testable sci-ence. Whatever happens, experiment will point the way to an-swering a 300-year-old question. By 2010 we will have madedecisive progress toward understanding why gravity is so weak.And we may find that we live in a strange Flatland, a membraneuniverse where quantum gravity is just around the corner.


The Theory Formerly Known as Strings. Michael Duff in ScientificAmerican, Vol. 278, No. 2, pages 64–69; February 1998.

The Elegant Universe: Superstrings, Hidden Dimensions, and theQuest for the Ultimate Theory. Brian Greene. W. W. Norton, 1999.

Flatland: A Romance of Many Dimensions. Edwin A. Abbott. Text is available from the Gutenberg project at ftp://ibiblio.org/pub/docs/books/gutenberg/etext94/flat11.txt

An introduction to tabletop gravity experiments is available athttp://mist.npl.washington.edu/eotwash/

An introduction to string theory is available athttp://superstringtheory.com/


TORSION OSCILLATOR at the University of Colorado looks for changes ingravity from 0.05 to 1.0 millimeter. Piezoelectrics vibrate the tungstensource mass (blue) like a diving board. Any forces acting between thesource mass and the tungsten detector (red) produce twisting oscillationsof the detector (inset; oscillations are exaggerated), which are sensed by

electronics. A gold-plated shield (yellow) suppresses electrostatic forces, and suspension from brass isolation stacks stops vibrations fromtraveling from the source to the detector. Electrostatic shields enclosingthe apparatus are not shown. For maximum sensitivity, liquid helium coolsthe apparatus to four kelvins.

Isolation stacks

Tilt stage

Source mass

Piezoelectric drive

Detector mass

Gold-plated shield

1 CENTIMETER


O n June 30, 2001, NASA

launched a Delta 2 rocketcarrying an 840-kilogram,four-meter-high spacecraft.Over the next three monthsthe Microwave Anisotropy

Probe (MAP) maneuvered into its orbitaround the sun, 1.5 million kilometers be-yond Earth’s orbit. MAP is now observingthe cosmic microwave background (CMB)radiation in exquisite detail over the entiresky. Because this radiation was emittednearly 15 billion years ago and has not in-teracted significantly with anything sincethen, getting a clear picture of the CMB isequivalent to seeing a map of the early uni-verse. By studying this map, scientists canlearn the composition, geometry and his-tory of the cosmos.

MAP is designed to measure the aniso-tropy of the CMB—the minuscule varia-tions in the temperature of the radiationcoming from different parts of the sky.MAP can record fluctuations as small as 20 millionths of a kel-vin from the radiation’s average temperature of 2.73 kelvins.What is more, the probe can detect hot and cold spots that sub-tend less than 0.23 degree across the sky, yielding a total ofabout one million measurements. Thus, MAP’s observations ofthe CMB will be far more detailed than the previous full-skymap, produced in the early 1990s by the Cosmic BackgroundExplorer (COBE), which was limited to a seven-degree angu-lar resolution.

One reason for the improvement is that MAP employs two

microwave telescopes, placed back-to-back, to focus the incom-ing radiation. The signals from the telescopes feed into 10 “dif-ferencing assemblies” that analyze five frequency bands in theCMB spectrum. But rather than measure the absolute temper-ature of the radiation, each assembly records the temperaturedifference between the signals from the two telescopes. Becausethe probe rotates, spinning once every two minutes and pre-cessing once every hour, the differencing assemblies comparethe temperature at each point in the sky with 1,000 other points,producing an interlocking set of data. The strategy is analogous


MAP’S BACK-TO-BACK TELESCOPES use primary and secondaryreflectors to focus the microwave radiation (red beams). The primary reflectors measure 1.6 by 1.4 meters, and thesecondary reflectors are one meter wide. Shielding on theback of the solar array (orange) blocks radiation from the sun,Earth and moon, preventing stray signals from entering theinstruments. The microwaves from each telescope stream into10 “feed horns” (beige cones) designed to sample fivefrequency bands. The four narrow horns at the center operateat 90 gigahertz, taking in microwaves with a three-millimeterwavelength. The wider horns at the periphery receive micro-waves of 22, 30, 40 and 60 gigahertz. At the base of each hornis a device that splits the radiation into two orthogonalpolarizations, which then feed into independent detectors.

cartographera cosmic

The MicrowaveAnisotropy Probe willgive cosmologists amuch sharper picture ofthe early universe

BY CHARLES L. BENNETT, GARY F. HINSHAW AND LYMAN PAGE

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to measuring the relative heights of bumps on a high plateaurather than recording each bump’s elevation above sea level.

This method cancels out errors resulting from slight changesin the temperature of the spacecraft itself. The overall calibra-tion of the data is done through a continuous measurement ofthe CMB dipole moment, the change in radiation temperaturecaused by Earth’s motion through the cosmos. The guiding prin-ciple of MAP’s design is to eliminate any spurious signals thatmight contaminate its measurements of the CMB. All indica-tions are that MAP will begin returning high-quality results in

January 2003, as scheduled. The cosmic map it will produce, ofunprecedented fidelity, will be MAP’s legacy for cosmology.


MAP’S OBSERVATION POST is near the L2 Lagrangepoint, which lies on the sun-Earth line about 1.5million kilometers beyond our planet. The probemoves around the L2 point while orbiting the sunat the same rate Earth does. This orbit ensuresthat MAP’s telescopes will always have anunobstructed view of deep space.

MAP IS LAUNCHED from the Kennedy SpaceCenter/Cape Canaveral Air Force Station.

MAP SCIENCE TEAM includes Charles L. Bennett (NASA Goddard Space FlightCenter), Mark Halpern (University of British Columbia), Gary F. Hinshaw(NASA GSFC), Norman C. Jarosik (Princeton University), Alan J. Kogut (NASAGSFC), Michele Limon (Princeton), Stephan S. Meyer (University of Chica-go), Lyman Page (Princeton), David N. Spergel (Princeton), Gregory S. Tuck-er (Brown University), David T. Wilkinson (Princeton), Edward J. Wollack(NASA GSFC) and Edward L. Wright (University of California, Los Angeles).

Sun

Phasing loopsEarth

L2

Lunar orbit

Moon at swing-by

1.5 million kilometers


Cosmologists are still asking the same questions thatthe first stargazers posed as they surveyed the heav-ens. Where did the universe come from? What, ifanything, preceded it? How did the universe arriveat its present state, and what will be its future? Al-though theorists have long speculated on the ori-

gin of the cosmos, until recently they had no way to probe theuniverse’s earliest moments to test their hypotheses. In recentyears, however, researchers have identified a method for ob-serving the universe as it was in the very first fraction of a sec-ond after the big bang. This method involves looking for tracesof gravitational waves in the cosmic microwave background(CMB), the cooled radiation that has permeated the universe fornearly 15 billion years.

The CMB was emitted about 400,000 years after the bigbang, when electrons and protons in the primordial plasma—

the hot, dense soup of subatomic particles that filled the earlyuniverse—first combined to form hydrogen atoms. Because thisradiation provides a snapshot of the universe at that time, it hasbecome the Rosetta stone of cosmology. After the CMB wasdiscovered in 1965, researchers found that its temperature—ameasure of the intensity of the black body radiation—was veryclose to 2.7 kelvins, no matter which direction they looked inthe sky. In other words, the CMB appeared to be isotropic,which indicated that the early universe was remarkably uni-form. In the early 1990s, though, a satellite called the CosmicBackground Explorer (COBE) detected minuscule variations—

only one part in 100,000—in the radiation’s temperature.These variations provide evidence of small lumps and bumpsin the primordial plasma. The inhomogeneities in the distrib-ution of mass later evolved into the large-scale structures of thecosmos: the galaxies and galaxy clusters that exist today.

In the late 1990s several ground-based and balloon-bornedetectors observed the CMB with much finer angular resolu-tion than COBE did, revealing structures in the primordial plas-ma that subtend less than one degree across the sky. (For com-parison, the moon subtends about half a degree.) The size ofthe primordial structures indicates that the geometry of the uni-verse is flat. The observations are also consistent with the the-ory of inflation, which postulates that an epoch of phenome-nally rapid cosmic expansion took place in the first few mo-ments after the big bang. In June 2001 NASA launched theMicrowave Anisotropy Probe (MAP), to extend the precise ob-servations of the CMB to the entire sky [see “A Cosmic Car-tographer,” on page 74]. Currently gathering data from itsdeep orbit 1.5 million kilometers beyond the earth, MAP is ex-pected to deliver its first scientific results by early 2003. The Eu-ropean Space Agency’s Planck spacecraft, to launch in 2007,will conduct an even more detailed mapping. Cosmologists ex-pect that the observations will unearth a treasure trove of in-formation about the early universe.

In particular, researchers are hoping to find direct evidenceof the epoch of inflation. The strongest evidence—the “smok-ing gun”—would be the observation of inflationary gravitation-


Scientists may soon glimpse the universe’sbeginnings by studying the subtle ripples

made by gravitational waves

BY ROBERT R. CALDWELL AND MARC KAMIONKOWSKI

Echoesfrom thebig bang

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DISTORTED UNIVERSEThe fantastically rapid expansion of the universe immediately after the big bang should have produced gravitationalwaves. These waves would have stretched and squeezed the primordial plasma, inducing motions in the spherical surfacethat emitted the cosmic microwave background, or CMB. These motions, in turn, would have caused redshifts andblueshifts in the radiation’s temperature and polarized the CMB. The illustration above shows the effects of a gravitationalwave traveling from pole to pole, with a wavelength that is one quarter the radius of the sphere.

GRAVITATIONAL WAVESAlthough gravitational waves have never been directly observed, theorypredicts that they can be detected because they stretch and squeeze thespace they travel through. On striking a spherical mass (a), a wave firststretches the mass in one direction and squeezes it in a perpendicular

direction (b). Then the effects are reversed (c), and the distortionsoscillate at the wave’s frequency (d and e). The distortions shown herehave been greatly exaggerated; gravitational waves are usually too weakto produce measurable effects.

a c db e


al waves. In 1918 Albert Einstein predict-ed the existence of gravitational waves asa consequence of his theory of general rel-ativity. They are analogues of electro-magnetic waves, such as x-rays, radiowaves and visible light, which are movingdisturbances of an electromagnetic field.Gravitational waves are moving distur-bances of a gravitational field. Like lightor radio waves, gravitational waves cancarry information and energy from thesources that produce them. Moreover,gravitational waves can travel unimped-ed through material that absorbs all formsof electromagnetic radiation. Just as x-rays allow doctors to peer through sub-stances that visible light cannot penetrate,

gravitational waves should allow re-searchers to view astrophysical phenom-ena that cannot be seen otherwise. Al-though gravitational waves have neverbeen directly detected, astronomical ob-servations have confirmed that pairs ofextremely dense objects such as neutronstars and black holes generate the wavesas they spiral toward each other.

The plasma that filled the universeduring its first 400,000 years was opaqueto electromagnetic radiation, because anyemitted photons were immediately scat-tered in the soup of subatomic particles.Therefore, astronomers cannot observeany electromagnetic signals dating frombefore the CMB. In contrast, gravita-

tional waves could propagate throughthe plasma. What is more, the theory ofinflation predicts that the explosive ex-pansion of the universe 10–38 second af-ter the big bang should have producedgravitational waves. If the theory is cor-rect, these waves would have echoedacross the early universe and, 400,000years later, left subtle ripples in the CMBthat can be observed today.

Waves from InflationTO UNDERSTAND HOW inflationcould have produced gravitational waves,let’s examine a fascinating consequenceof quantum mechanics: empty space isnot so empty. Virtual pairs of particlesare spontaneously created and destroyedall the time. The Heisenberg uncertaintyprinciple declares that a pair of particleswith energy ∆E may pop into existencefor a time ∆t before they annihilate eachother, provided that ∆E ∆t < h/2, whereh is the reduced Planck’s constant (1.055× 10–34 joule-second). You need not wor-ry, though, about virtual apples or ba-nanas popping out of empty space, be-cause the formula applies only to ele-mentary particles and not to complicatedarrangements of atoms.

One of the elementary particles af-fected by this process is the graviton, thequantum particle of gravitational waves(analogous to the photon for electro-magnetic waves). Pairs of virtual gravi-tons are constantly popping in and out ofexistence. During inflation, however, thevirtual gravitons would have been pulledapart much faster than they could havedisappeared back into the vacuum. Inessence, the virtual particles would havebecome real particles. Furthermore, thefantastically rapid expansion of the uni-verse would have stretched the gravitonwavelengths from microscopic to macro-scopic lengths. In this way, inflationwould have pumped energy into the pro-duction of gravitons, generating a spec-trum of gravitational waves that reflect-ed the conditions in the universe in thosefirst moments after the big bang. If infla-tionary gravitational waves do indeed ex-ist, they would be the oldest relic in theuniverse, created 400,000 years beforethe CMB was emitted. AL

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COSMIC TIME LINEDuring the epoch of inflation—the tremendous expansion of the universe that took place in the first moments after the big bang—quantum processes generated a spectrum of gravitational waves.The waves echoed through the primordial plasma, distorting the CMB radiation that was emitted about 400,000 years later. By carefully observing the CMB today, cosmologists may detect theplasma motions induced by the inflationary waves.

15 billion years

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Whereas the microwave radiation inthe CMB is largely confined to wave-lengths between one and five millimeters(with a peak intensity at two millime-ters), the wavelengths of the inflationarygravitational waves would span a muchbroader range: one centimeter to 1023

kilometers, which is the size of the pres-ent-day observable universe. The theoryof inflation stipulates that the gravita-tional waves with the longest wave-lengths would be the most intense andthat their strength would depend on therate at which the universe expanded dur-ing the inflationary epoch. This rate isproportional to the energy scale of infla-tion, which was determined by the tem-perature of the universe when inflationbegan. And because the universe washotter at earlier times, the strength of thegravitational waves ultimately dependson the time at which inflation started.

Unfortunately, cosmologists cannotpinpoint this time, because they do notknow in detail what caused inflation.Some physicists have theorized that in-flation started when three of the funda-mental interactions—the strong, weakand electromagnetic forces—became dis-sociated soon after the universe’s cre-ation. According to this theory, the threeforces were one and the same at the very

beginning but became distinct 10–38 sec-ond after the big bang, and this eventsomehow triggered the sudden expansionof the cosmos. If the theory is correct, in-flation would have had an energy scale of1015 to 1016 GeV. (One GeV is the ener-gy a proton would acquire while beingaccelerated through a voltage drop of onebillion volts. The largest particle acceler-ators currently reach energies of 103

GeV.) On the other hand, if inflationwere triggered by another physical phe-nomenon occurring at a later time, thegravitational waves would be weaker.

Once produced during the first frac-tion of a second after the big bang, the in-flationary gravitational waves wouldpropagate forever, so they should still berunning across the universe. But how cancosmologists observe them? First consid-er how an ordinary stereo receiver detectsa radio signal. The radio waves consist ofoscillating electrical and magnetic fields,which cause the electrons in the receiver’s

antenna to move back and forth. Themotions of these electrons produce anelectric current that the receiver records.

Similarly, a gravitational wave can in-duce an oscillatory stretching and squeez-ing of the space it travels through. Theseoscillations would cause small motions ina set of freely floating test masses. In thelate 1950s physicist Hermann Bondi ofKing’s College London tried to convinceskeptics of the physical reality of suchwaves by describing a hypothetical grav-itational-wave detector. The idealized ap-paratus was a pair of rings hanging freelyon a long, rigid bar. An incoming gravi-tational wave of amplitude h and fre-quency f would cause the distance L be-tween the two rings to alternately con-tract and expand by an amount h × L,with a frequency f. The heat from thefriction of the rings rubbing against thebar would provide evidence that thegravitational wave carries energy.

Researchers are currently building so-phisticated gravitational-wave detectors,which will use lasers to track the tiny mo-tions of suspended masses [see box onnext page]. The distance between the testmasses determines the band of wave-


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ROBERT R. CALDWELL and MARC KAMIONKOWSKI were both physics majors in the class of1987 at Washington University. Caldwell earned his Ph.D. in physics at the University ofWisconsin–Milwaukee in 1992. One of the chief formulators of the theory of quintessence,Caldwell is now assistant professor of physics and astronomy at Dartmouth College. Kami-onkowski earned his doctorate in physics at the University of Chicago in 1991. Now pro-fessor of theoretical physics and astrophysics at the California Institute of Technology,he received the Warner Prize in 1998 for his contributions to theoretical astronomy.

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RELIC IN THE RADIATIONInflationary gravitational waves would have left a distinctive imprint on the CMB. This illustrationdepicts the simulated temperature variations and polarization patterns that would result from thedistortions shown in the bottom illustration on page 77. The red and blue spots represent colder andhotter regions of the CMB, and the small line segments indicate the orientation angle of thepolarization in each region of the sky.


lengths that the devices can monitor. Thelargest of the ground-based detectors,which has a separation of four kilometersbetween the masses, will be able to mea-sure the oscillations caused by gravita-tional waves with wavelengths from 30 to30,000 kilometers; a planned space-basedobservatory may be able to detect wave-lengths about 1,000 times longer. Thegravitational waves generated by neutronstar mergers and black hole collisionshave wavelengths in this range, so theycan be detected by the new instruments.But the inflationary gravitational waves inthis range are much too weak to producemeasurable oscillations in the detectors.

The strongest inflationary gravitation-al waves are those with the longest wave-lengths, comparable to the diameter of theobservable universe. To detect thesewaves, researchers need to observe a set of

freely floating test masses separated bysimilarly large distances. Serendipitously,nature has provided just such an arrange-ment: the primordial plasma that emit-ted the CMB radiation. During the400,000 years between the epoch of in-flation and the emission of the CMB, theultralong-wavelength gravitational wavesechoed across the early universe, alter-nately stretching and squeezing the plasma[see illustration on page 78]. Researcherscan observe these oscillatory motions to-day by looking for slight Doppler shiftsin the CMB.

If, at the time when the CMB wasemitted, a gravitational wave was stretch-ing a region of plasma toward us—that is,toward the part of the universe thatwould eventually become our galaxy—

the radiation from that region will appearbluer to observers because it has shifted

to shorter wavelengths (and hence a high-er temperature). Conversely, if a gravita-tional wave was squeezing a region ofplasma away from us when the CMB wasemitted, the radiation will appear redderbecause it has shifted to longer wave-lengths (and a lower temperature). Bysurveying the blue and red spots in theCMB—which correspond to hotter andcolder radiation temperatures—research-ers could conceivably see the pattern ofplasma motions induced by the inflation-ary gravitational waves. The universe itselfbecomes a gravitational-wave detector.

Particulars of PolarizationTHE TASK IS NOT so simple, however.As we noted at the beginning of this arti-cle, mass inhomogeneities in the early uni-verse also produced temperature varia-tions in the CMB. (For example, the grav-itational field of the denser regions ofplasma would have redshifted the pho-tons emitted from those regions, produc-ing some of the temperature differencesobserved by COBE.) If cosmologists lookat the radiation temperature alone, theycannot tell what fraction (if any) of thevariations should be attributed to gravi-tational waves. Even so, scientists at leastknow that gravitational waves could nothave produced any more than the one-in-100,000 temperature differences observedby COBE and the other CMB radiationdetectors. This fact puts an interestingconstraint on the physical phenomenathat gave rise to inflation: the energy scaleof inflation must be less than about 1016

GeV, and therefore the epoch could nothave occurred earlier than 10–38 secondafter the big bang.

But how can cosmologists go further?How can they get around the uncertain-ty over the origin of the temperature fluc-tuations? The answer lies with the polar-ization of the CMB. When light strikes asurface in such a way that the light scat-ters at nearly a right angle from the orig-inal beam, it becomes linearly polarized—

that is, the waves become oriented in aparticular direction. This is the effect thatpolarized sunglasses exploit: because thesunlight that scatters off the ground istypically polarized in a horizontal direc-tion, the filters in the glasses reduce the AL

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THE GRAVITATIONAL WAVESproduced by quantumprocesses during theinflationary epoch are by nomeans the only ones believedto be traveling across theuniverse. Many astrophysicalsystems, such as orbitingbinary stars, merging neutronstars and colliding black holes,should also emit powerfulgravitational waves.

The problem with detectingthe waves is that their strength

fades as they spread outward while traveling hundreds of millions of light-years to theearth. To measure such minuscule oscillations, researchers are preparing the LaserInterferometer Gravitational-Wave Observatory (LIGO), which consists of facilities inLivingston, La. (above), and Hanford, Wash. Results from the facilities will be comparedto rule out local effects that mimic gravitational waves, such as seismic activity,acoustic noise and laser instabilities [see “Ripples in Spacetime,” on page 88].

Physicists are also building smaller detectors that will work in tandem with LIGO,allowing researchers to triangulate the sources of gravitational waves. Examples ofthese observatories are TAMA (near Tokyo), Virgo (near Pisa, Italy) and GEO (nearHannover, Germany). And to monitor gravitational waves with longer wavelengths, NASAand the European Space Agency are planning to launch the Laser Interferometer SpaceAntenna in 2010. Unfortunately, none of these proposed observatories will be sensitiveenough to detect the gravitational waves produced by inflation. Only the cosmicmicrowave background radiation can reveal their presence. —R.R.C. and M.K.

Wave HuntersNew detectors will soon be ready

Livingston, La.


glare by blocking light waves with thisorientation. The CMB is polarized aswell. Just before the early universe be-came transparent to radiation, the CMBphotons scattered off the electrons in theplasma for the last time. Some of thesephotons struck the particles at large an-gles, which polarized the radiation.

The key to detecting the inflationarygravitational waves is the fact that theplasma motions caused by the waves pro-duced a different pattern of polarizationthan the mass inhomogeneities did. Theidea is relatively simple. The linear po-larization of the CMB can be depictedwith small line segments that show theorientation angle of the polarization ineach region of the sky [see illustration onpage 79]. These line segments are some-times arranged in rings or in radial pat-terns. The segments can also appear in ro-tating swirls that are either right- or left-handed—that is, they seem to be turningclockwise or counterclockwise [see illus-tration at right].

The “handedness” of these patterns isthe clue to their origin. The mass inho-mogeneities in the primordial plasmacould not have produced such polariza-tion patterns, because the dense and rar-efied regions of plasma had no right- orleft-handed orientation. In contrast, grav-itational waves do have a handedness:they propagate with either a right- or left-handed screw motion. The polarizationpattern produced by gravitational waveswill look like a random superposition ofmany rotating swirls of various sizes. Re-searchers describe these patterns as hav-ing a curl, whereas the ringlike and radi-al patterns produced by mass inhomo-geneities have no curl.

Not even the most keen-eyed observ-er can look at a polarization diagram,such as the one shown on page 79, andtell by eye whether it contains any pat-terns with curls. But an extension ofFourier analysis—a mathematical tech-nique that can break up an image into aseries of waveforms—can be used to di-vide a polarization pattern into its con-stituent curl and curl-free patterns. Thus,if cosmologists can measure the CMB po-larization and determine what fractioncame from curl patterns, they can calcu-

late the amplitude of the ultralong-wave-length inflationary gravitational waves.Because the amplitude of the waves wasdetermined by the energy of inflation, re-searchers will get a direct measurement ofthat energy scale. This finding, in turn,will help answer the question of whetherinflation was triggered by the unificationof fundamental forces.

What are the prospects for detectingthe gentle rings and curls and swirls of thepolarized CMB sky? That is the next goalof CMB scientists. Although theorists areconfident that the relic radiation is polar-ized, observational verification has elud-ed researchers. Roughly a dozen experi-ments worldwide are striving to measurethe variation of the polarization pattern,and we can expect exciting results soon.But theorists also predict that the strengthof the curl-free polarization componentis much stronger than the curl compo-nent—the “smoking gun” of the infla-tionary gravitational waves we have de-scribed. So though there is a good chancethe MAP satellite or one of the ground-or balloon-based experiments will detectthe CMB’s curl-free polarization withinthe next year, the curl component will re-main just out of reach.

Subsequent experiments may have abetter chance. If inflation was indeedcaused by the unification of forces, itsgravitational-wave signal may be strongenough to be detected by the Planck satel-lite, although an even more sensitivenext-generation spacecraft might beneeded. CMB scientists are already work-ing with NASA to plan such a mission: theCosmic Microwave Background Polar-ization Experiment (CMBPOL), whichwould fly sometime after 2014. If the in-flationary theory is true, and there are ul-tralong-wavelength gravitational wavesof primordial origin coursing through the

cosmos, then CMBPOL will be able tosense the telltale signs of the squeezingand stretching of the plasma at last scat-tering. The discovery would extend ourunderstanding of the universe back to theearliest fraction of a second after the bigbang. But if inflation was triggered byother physical phenomena occurring atlater times and lower energies, the signalfrom the gravitational waves will be fartoo weak to be detected in the foreseeablefuture.

Because cosmologists are not certainabout the origin of inflation, they cannotdefinitively predict the strength of the po-larization signal produced by inflationarygravitational waves. But if there is evena small chance that the signal is de-tectable, then it is worth pursuing. Its de-tection would not only provide incontro-vertible evidence of inflation but also giveus the extraordinary opportunity to lookback at the very earliest times, just 10–38

second after the big bang. We could thencontemplate addressing one of the mostcompelling questions of the ages: Wheredid the universe come from?


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POLARIZATION PATTERNSThe polarization of the CMB may hold importantclues to the history of the early universe.Density variations in the primordial plasmawould cause ringlike and radial patterns ofpolarization (top). Gravitational waves, incontrast, would produce right- and left-handedswirls (bottom).

First Space-Based Gravitational-Wave Detectors. Robert R. Caldwell, Marc Kamionkowski andLeven Wadley in Physical Review D, Vol. 59, Issue 2, pages 27101–27300; January 15, 1999.

Recent observations of the cosmic microwave background are described at these Web sites:pupgg.princeton.edu/~cmb/; www.physics.ucsb.edu/~boomerang/;cosmology.berkeley.edu/group/cmb/

Details of the MAP and Planck missions are available at map.gsfc.nasa.gov/;astro.estec.esa.nl/astrogen/planck/mission–top.html

More information on gravitational-wave detectors is available at www.ligo.caltech.edu;lisa.jpl.nasa.gov



is preeminently a 20th-century achievement. Only in the1920s did we realize that our Milky Way, with its 100 billionstars, is just one galaxy among millions. Our empirical knowl-edge of the universe has been accumulating ever since. We cannow set our entire solar system in a grand evolutionary con-text, tracing its constituent atoms back to the initial instants ofthe big bang. If we were ever to discover alien intelligences, onething we might share with them—perhaps the only thing—

would be a common interest in the cosmos from which we haveall emerged.

Using the current generation of ground-based and orbitalobservatories, astronomers can look back into the past and seeplain evidence of the evolution of the universe. Marvelous im-ages from the Hubble Space Telescope reveal galaxies as theywere in remote times: balls of glowing, diffuse gas dotted withmassive, fast-burning blue stars. These stars transmuted thepristine hydrogen from the big bang into heavier atoms, andwhen the stars died they seeded their galaxies with the basicbuilding blocks of planets and life—carbon, oxygen, iron andso on. A Creator didn’t have to turn 92 different knobs to make

all the naturally occurring elements in the periodic table. In-stead the galaxies act as immense ecosystems, forging elementsand recycling gas through successive generations of stars. Thehuman race itself is composed of stardust—or, less romanti-cally, the nuclear waste from the fuel that makes stars shine.

Astronomers have also learned much about the earlier, pre-galactic era by studying the microwave background radiation thatmakes even intergalactic space slightly warm. This afterglow ofcreation tells us that the entire universe was once hotter than thecenters of stars. Scientists can use laboratory data to calculatehow much nuclear fusion would have happened during the firstfew minutes after the big bang. The predicted proportions ofhydrogen, deuterium and helium accord well with what as-tronomers have observed, thereby corroborating the big bangtheory.

At first sight, attempts to fathom the cosmos might seem

Cosmic exploration

IN T HIS C E N T U RY COS MOLO GIS T S W ILL U N R AV E L T H E MYS T E RY OF OU R U NI V E R S E ’ S BIRT H —

BY MARTIN REES

Our Universe

and OthersA N D PE R H A P S PROV E T H E E XIS T E NC E OF OT H E R

U NI V E R S E S A S W E LL

Exploring

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LARGE-SCALE STRUCTURE of the universe can be simulated by runningcosmological models on a supercomputer. In this simulation,

produced by the Virgo Consortium, each particle represents a galaxy.

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presumptuous and premature, even at the start of the 21st cen-tury. Cosmologists have, nonetheless, made remarkable prog-ress in recent years. This is because what makes things bafflingis their degree of complexity, not their sheer size—and a star issimpler than an insect. The fierce heat within stars, and in theearly universe, guarantees that everything breaks down into itssimplest constituents. It is the biologists, whose role it is to studythe intricate multilayered structure of trees, butterflies andbrains, who face the tougher challenge.

The progress in cosmology has brought new mysteries intosharper focus and raised questions that will challenge as-tronomers well into this century. For example, why does ouruniverse contain its observed mix of ingredients? And how,from its dense beginnings, did it heave itself up to such a vast

size? The answers will take us beyond the physics with whichwe are familiar and will require new insights into the nature ofspace and time. To truly understand the history of the universe,scientists must discover the profound links between the cosmicrealm of the very large and the quantum world of the very small.

It is embarrassing to admit, but astronomers still don’t knowwhat our universe is made of. The objects that emit radiationthat we can observe—such as stars, quasars and galaxies—con-stitute only a small fraction of the universe’s matter. The vastbulk of matter is dark and unaccounted for. Most cosmologistsbelieve dark matter is composed of weakly interacting particlesleft over from the big bang, but it could be something even moreexotic. Whatever the case, it is clear that galaxies, stars and plan-ets are a mere afterthought in a cosmos dominated by quite dif-ferent stuff. Searches for dark matter, mainly via sensitive un-

derground experiments designed to detect elusive subatomicparticles, will continue apace in this decade. The stakes are high:success would not only tell us what most of the universe is madeof but would also probably reveal some fundamentally newkinds of particles.

The ultimate fate of our universe—whether it continues ex-panding indefinitely or eventually changes course and collapsesto the so-called big crunch—depends on the total amount of darkmatter and the gravity it exerts. Current data indicate that theuniverse contains only about 30 percent of the matter that wouldbe needed to halt the expansion. (In cosmologists’ jargon,omega—the ratio of observed density to critical density—is 0.3.)The odds favoring perpetual growth have recently strengthenedfurther: tantalizing observations of distant supernovae suggest

that the expansion of the universe may be speeding up ratherthan slowing down. These observations may indicate that an ex-tra force overwhelms gravity on cosmic scales—a phenomenonperhaps related to what Albert Einstein called the cosmologicalconstant, a form of energy latent in empty space itself that (un-like ordinary matter) has negative pressure and causes a repul-sion. Studies of small nonuniformities in the background radia-tion reveal that our universe is “flat”—in the sense that the an-gles of a large triangle drawn in space add up to 180 degrees.Taken in conjunction with one another, these lines of evidencesuggest that 5 percent of our universe (or slightly less) is com-posed of ordinary atoms, about 25 percent is dark matter andthe other 70 percent is the even more perplexing dark energy.

Research is also likely to focus on the evolution of the uni-verse’s large-scale structure. If one had to answer the question


The big bang

10–43 second Quantum gravity era

10–36 second Probable era of inflation

10–5 second Formation of protons and neutrons from quarks

3 minutesSynthesis ofhelium nuclei

300,000 yearsFirst atoms form

The great mystery for cosmologists is the series of events that occurred less than one millisecond after the big bang.

COSMIC TIME LINE shows theevolution of our universe from thebig bang to the present day. Inthe first instant of creation—theepoch of inflation—the universeexpanded at a staggering rate.After about three minutes, theplasma of particles and radiationcooled enough to allow theformation of simple atomicnuclei; after another 300,000years, atoms of hydrogen andhelium began to form. The firststars and galaxies appearedabout a billion years later. Theultimate fate of the universe—whether it will expand forever orrecollapse—is still unknown,although current evidence favorsperpetual expansion.


“What’s been happening since the big bang?” in just one sen-tence, the best response might be to take a deep breath and say,“Ever since the beginning, gravity has been amplifying inho-mogeneities, building up structures and enhancing temperaturecontrasts—a prerequisite for the emergence of the complexitythat lies around us now and of which we’re a part.” Astron-omers are now learning more about this 10-billion-year processby creating virtual universes on their computers. In the comingyears, they will be able to simulate the history of the universewith ever improving realism and then compare the results withwhat telescopes reveal.

Questions of structure have preoccupied astronomers sincethe time of Isaac Newton, who wondered why all the planetscircled the sun in the same direction and in almost the sameplane. In his 1704 work Opticks he wrote: “Blind fate couldnever make all the planets move one and the same way in orbitsconcentrick.” Such a wonderful uniformity in the planetary sys-tem, Newton believed, must be the effect of divine providence.

Now astronomers know that the coplanarity of the planetsis a natural outcome of the solar system’s origin as a spinningdisk of gas and dust. Indeed, we have extended the frontiersof our knowledge to far earlier times; cosmologists can rough-ly outline the history of the universe back to the first second af-ter the big bang. Conceptually, however, we’re in little bettershape than Newton was. Our understanding of the causal chainof events now stretches further back in time, but we still runinto a barrier, just as surely as Newton did. The great mysteryfor cosmologists is the series of events that occurred less thanone millisecond after the big bang, when the universe was ex-traordinarily small, hot and dense. The laws of physics withwhich we are familiar offer little firm guidance for explainingwhat happened during this critical period.

To unravel this mystery, cosmologists must first pin down—

by improving and refining current observations—some of thecharacteristics of the universe when it was only one second old:its expansion rate, the size of its density fluctuations, and its pro-portions of ordinary atoms, dark matter and radiation. But tocomprehend why our universe was set up this way, we mustprobe further back, to the first tiny fraction of a microsecond.Such an effort will require theoretical advances. Physicists mustdiscover a way to relate Einstein’s theory of general relativity,which governs large-scale interactions in the cosmos, to thequantum principles that apply at very short distances. A unified

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MULTIPLE UNIVERSES are continually being born, according to somecosmologists. Each universe is shown here as an expanding bubble

branching off from its parent universe. The changes in color representshifts in the laws of physics from one universe to another.

1 billion yearsFirst stars, galaxies andquasars appear 10 billion to 15 billion years

Modern galaxies appear

Perpetual expansion

Recollapse

w w w . s c i a m . c o m COPYRIGHT 2002 SCIENTIFIC AMERICAN, INC.

theory would be needed to explain what happened in the firstcrucial moments after the big bang, when the entire universe wassqueezed into a space smaller than a single atom.

Astronomy is a subject in which observation is king. Nowthe same is true for cosmology—in contrast with the pre-1965era, when speculation was largely unconstrained. The answersto many of cosmology’s long-standing questions are most like-ly to come from the telescopes that have recently gone into use.The two Keck Telescopes on Mauna Kea in Hawaii are far moresensitive than earlier observatories and thus can glimpse fainterobjects. Still more impressive is the European Southern Obser-vatory’s Very Large Telescope at Paranal in northern Chile—alinked array of four telescopes, each with mirrors eight metersin diameter. In space, astronomers can take advantage of theChandra X-ray Observatory and its European counterpart,XMM-Newton. Several new instruments are under construc-tion to detect radio waves, infrared emissions and cosmic rays.And a decade from now next-generation space telescopes willcarry the enterprise far beyond what the Hubble can achieve.

Well before 2050 we will probably see the construction of

giant observatories in space or perhaps on the far side of themoon. The sensitivity and imaging power of these arrays willvastly surpass that of any instruments now in use. The new tele-scopes will target black holes and planets in other solar systems.They will also provide snapshots of every cosmological era go-ing back to the very first light, when the earliest stars (or maybequasars) condensed out of the expanding debris from the bigbang. Some of these observatories may even be able to measuregravitational waves, allowing scientists to probe vibrations inthe fabric of spacetime itself.

The amount of data provided by all these instruments willbe so colossal that the entire process of analysis and discoverywill most likely be automated. Astronomers will focus their at-tention on heavily processed statistics for each population of ob-jects they are studying and in this way find the best examples—

for instance, the planets in other solar systems that are most likeEarth. Researchers will also concentrate on extreme objects thatmay hold clues to physical processes that are not yet fully un-derstood. One such object is the gamma-ray burster, whichemits, for a few seconds, as much power as a billion galaxies.Increasingly, astronomers will use the heavens as a cosmic lab-oratory to probe phenomena that cannot be simulated on Earth.

Another benefit of automation will be open access to astro-nomical data that in the past were available to only a privilegedfew. Detailed maps of the sky will be available to anyone whocan access or download them. Enthusiasts anywhere in theworld will be able to check their own hunches, seek new pat-terns and discover unusual objects.

Intimations of a Multiverse? COSMOLOGISTS VIEW the universe as an intricate tapestrythat has evolved from initial conditions that were imprinted inthe first microsecond after the big bang. Complex structures andphenomena have unfolded from simple physical laws—wewouldn’t be here if they hadn’t. Simple laws, however, do not


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LUNAR OBSERVATORIES will greatly extend the reach of 21st-centuryastronomers. The far side of the moon is an ideal place for telescopesbecause of its absence of atmosphere and its utterly dark nights, free of reflected sun and radio transmissions from Earth. Lunar ores can be used to build the instruments.

MARTIN REES is Royal Society Research Professor at the Universi-ty of Cambridge and holds the honorary title of Astronomer Royal.He was previously director of the Cambridge Institute of Astrono-my and before that a professor at the University of Sussex. His re-search interests include black holes, galaxy formation and high-en-ergy astrophysics. He also lectures and writes extensively for gen-eral audiences. His recent books are Before the Beginning (PerseusPublishing, 1998), Just Six Numbers (Basic Books, 2000) and OurCosmic Habitat (Princeton University Press, 2001).

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necessarily lead to complex consequences. Consider an ana-logue from the field of fractal mathematics: the Mandelbrot set,a pattern with an infinite depth of structure, is encoded by ashort algorithm, but other simple algorithms that are super-ficially similar yield very boring patterns.

Our universe could not have become structured if it were notexpanding at a special rate. If the big bang had produced fewerdensity fluctuations, the universe would have remained dark,with no galaxies or stars. And there are other prerequisites forcomplexity. If our universe had more than three spatial dimen-sions, planets could not stay in orbits around stars. If gravitywere much stronger, it would crush living organisms of humansize, and stars would be small and short-lived. If nuclear forceswere a few percent weaker, only hydrogen would be stable:there would be no periodic table, no chemistry and no life.

Some would argue that this fine-tuning of the universe,which seems so providential, is nothing to be surprised about,because we could not exist otherwise. There is, however, an-

other interpretation: many universes may exist, but only somewould allow creatures like us to emerge.

Perhaps, then, our big bang wasn’t the only one. This spec-ulation dramatically enlarges our concept of reality. The entirehistory of our universe becomes just an episode, a single facet,of the infinite multiverse. Some universes might resemble ours,but most would recollapse after a brief existence, or the lawsgoverning them would not permit complex consequences.

Some cosmologists, especially Andrei Linde of Stanford Uni-versity and Alex Vilenkin of Tufts University, have alreadyshown how certain mathematical assumptions lead to the cre-ation of a multiverse. But such ideas will remain on the specu-lative fringe of cosmology until we really understand—ratherthan just guess at—the extreme physics that prevailed immedi-ately after the big bang. Will the long-awaited unified theoryuniquely determine the masses of particles and the strengths ofthe basic forces? Or are these properties accidental outcomes ofhow our universe cooled—secondary manifestations of stilldeeper laws governing an entire ensemble of universes?

This topic might seem arcane, but the status of multiverseideas affects how we should place our bets in some ongoing cos-mological controversies. Some theorists have a strong prefer-ence for the simplest picture of the cosmos, which would requirean omega of 1—the universe would be just dense enough to haltits own expansion. They are unhappy with observations sug-gesting that the universe is not nearly so dense and with extracomplications such as the cosmological constant and dark en-ergy. Perhaps we should draw a lesson from 17th-century as-tronomers Johannes Kepler and Galileo Galilei, who were up-set to find that planetary orbits were elliptical. Circles, theythought, were simpler and more beautiful. But Newton later ex-

plained all orbits in terms of a simple, universal law of gravity.Had Galileo still been alive, he surely would have been joyfullyreconciled to ellipses.

The parallel is obvious. If a low-density universe with a cos-mological constant seems ugly, maybe this shows our limited vi-sion. Just as Earth follows one of the few Keplerian orbitsaround the sun that allow it to be habitable, our universe maybe one of the few habitable members of a grander ensemble.

The Next ChallengesSCIENTISTS ARE EXPANDING humanity’s store of knowl-edge on three great frontiers: the very big, the very small and thevery complex. Cosmology involves them all. In the comingyears, researchers will focus on pinning down the basic univer-sal constants, such as omega, and on discovering what darkmatter is. I think there is a good chance of achieving both goalswithin 10 years. Maybe everything will fit the standard theo-retical framework, and we will successfully determine not only

the relative abundance of ordinary atoms and dark matter in theuniverse but also the cosmological constant and the primordialdensity fluctuations. If that happens, we will have taken the mea-sure of our universe just as we have learned the size and shapeof Earth and our sun. On the other hand, our universe may turnout to be too complicated to fit the standard framework. Somemay describe the first outcome as optimistic; others may preferto inhabit a more complicated and challenging place!

In addition, theorists must elucidate the exotic physics of thevery earliest moments of the universe. If they succeed, we willlearn whether there are many universes and which features ofour universe are mere contingencies rather than the necessaryoutcomes of the deepest laws. Our understanding will still havelimits, however. Physicists may someday discover a unified the-ory that governs all of physical reality, but they will never beable to tell us what breathes fire into their equations and whatactualizes them in a real cosmos.

Cosmology is not only a fundamental science; it is also thegrandest of the environmental sciences. How did a hot, amor-phous fireball evolve, over 10 billion to 15 billion years, into ourcomplex cosmos of galaxies, stars and planets? How did atomsassemble—here on Earth and perhaps on other worlds—into liv-ing beings intricate enough to ponder their own origins? Thesequestions are a challenge for this millennium. Answering themmay well be an unending quest.

Planet Quest: The Epic Discovery of Alien Solar Systems. Ken Croswell.Free Press, 1997.

The Little Book of the Big Bang: A Cosmic Primer. Craig J. Hogan.Copernicus, 1998.


Perhaps our big bang wasn’t the only one;many universes may exist in the infinite multiverse.


BIRTH WAILS AND DEATH THROES of celestial titans—such as the black holes (spheres) colliding in this supercomputer simulation—rumble through the universeon waves of gravitational energy. This year new instruments of astonishing sizeand sensitivity are trying to tune in those signals for the first time.

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w w w . s c i a m . c o m U p d a t e d f r o m t h e A p r i l 2 0 0 2 i s s u e 89

HANFORD, WASH., AND LIVINGSTON, LA.—A chill January wind sendsa shiver through Frederick J. Raab as he stands, binoculars to his eyes, on amound near the center of the LIGO Hanford Observatory. He runs his gazenorthward down a ruler-straight concrete tunnel to a building four kilome-

ters to the north: there is one end of the observatory. Pivoting 90 degrees, Raab panswestward across the sagebrush-stubbled desert until he spots an identical tube and an-other building, also four kilometers distant. “When we talk about locking the laserbeam” that shines inside those tubes, Raab says, “we mean holding the light wavessteady to better than the width of an atom—over that distance.”

Raab oversaw the construction of this giant try square, one of a pair that are thelargest, most expensive and—if they fulfill the ambition of their designers—most sen-sitive detectors yet to join the 40-year hunt for gravitational waves. Part ruler, partclock, these two instruments are spacetime meters that will attempt to record how the

IN SPACETIMEPHYSICISTS HAVE SPENT EIGHT YEARS AND $365 MILLION BUILDING

A RADICALLY NEW KIND OF OBSERVATORY TO DETECT GRAVITATIONAL

WAVES. BUT WILL IT WORK? A TRIAL RUN PUT IT TO THE TEST

BY W. WAYT GIBBS


continuum is rattled by the most violentcataclysms in the universe: detonatingstars, colliding black holes, perhaps phe-nomena not yet imagined. As these rip-ples expand outward at the speed oflight, they alternately stretch and squeezespace, causing the distance between free-floating objects to expand and contract.But by the time the vibrations reach theearth, theorists estimate, they are so un-substantial that they alter distances byless than one part in a trillion billion.

For all the cutting-edge technology

crammed into LIGO, it is not yet clearwhether it can attain that incredible sen-sitivity. Reduced to such a tiny murmur,the mightiest cosmic events are easilyoverpowered by the gentlest mundanedisturbance. “The tide deforms the earth’scrust as well as the oceans,” Raab tells me.It moves the buildings here by a third of amillimeter, 100 billion times the displace-ment a gravitational wave would cause.Every earthquake in the world over mag-nitude six, the rumble of every truck onnearby roads, the computer fans in the labnext door—all these things shake theground by more than an atom’s width.“Even engine noise from jets passing over-head can work its way in,” Raab says.

Down in the control room, we watchas the instrument struggles to compensatefor the thumps and bumps. Fourteendays into an 18-day test run that beganon December 28, the noise is winning.Raab stares at a panel of graphs project-

ed onto the far wall. A red line bouncesup and down, charting the status of themain detector here as it is thrown out ofwhack, steadies itself and gets knockedout again a few minutes later. A blue linethat represents a smaller quality-controldetector has gone flat altogether.

During a teleconference, physicist H.Richard Gustafson troubleshoots glitch-es with his counterparts at the LIGO Liv-ingston Observatory, which sits in thebackwoods of Louisiana. Joining theconversation is the director of the GEO

600, a similar but smaller instrumentnear Hannover, Germany. “Here at Han-ford we had an awful night,” Gustafsonsays, recounting troubles with computercrashes and noisy electronics.

The instrument in Louisiana has beenmore predictable. During the night it runssmoothly, but at 6:30 A.M. its line on thecontrol screen goes flat as morning trafficpicks up on Interstate 12 a few miles fromthe observatory and as Weyerhaeuserloggers begin felling loblolly pines near-by. GEO, with its shorter, 600-meterarms and less demanding precision, hasbeen a model of reliability, on duty morethan 90 percent of the time. But scientistsneed all three instruments up and run-ning, and over two weeks the best stretchof simultaneous operation lasted justover an hour and a half.

Szabolcs Márka, a 32-year-old Hun-garian postdoc at LIGO Livingston,seems content with the progress so far on

this test run, the fifth that he has managedand the last before the two instrumentswere to begin routine round-the-clockobservations in May. “As usual we are inproblem-solving mode,” Márka says.

Labor Pains, Death GaspsEVER SINCE THE FOUNDERS of theLIGO project—Kip S. Thorne and Ron-ald Drever of the California Institute ofTechnology and Rainer Weiss of theMassachusetts Institute of Technology—

first proposed the Laser Interferometer

Gravitational Wave Observatory in 1984,no one has doubted that only a Herculeanfeat of engineering would make it work.That is one reason that “the project facedtremendous opposition from astron-omers,” says Harry M. Collins, a sociolo-gist at Cardiff University in Wales who hasstudied the field’s halting expansion froma backwater of physics to Big Science.

“The National Science Foundationturned down our first two proposals,”Thorne remembers. “And the third, sub-mitted in 1989, went through five years ofvery extensive review.” High-profile as-tronomers, notably Jeremiah P. Ostrikerof Princeton University, objected to thesteep price, which by 1993 had risen to$250 million. They feared that smallerand less risky projects would get elbowedout of the budget. A blue-ribbon panel setup to rank U.S. astronomers’ priorities forthe 1990s excluded LIGO from its wishlist. “It was a unanimous decision,” re-calls John Bahcall, an astrophysicist at theInstitute for Advanced Studies in Prince-ton, N.J., who chaired the committee.Congress passed on the LIGO proposal atfirst, not approving funding until 1994.

Thorne and other proponents ofLIGO argued that gravitational signalscould launch a whole new field of as-tronomy, because they carry informationabout the universe that scientists cangather in no other way. These etherealripples were predicted in 1918 by AlbertEinstein, who saw them as an unavoid-


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Although astronomers have never detected gravitational waves directly,Einstein’s theory of relativity predicts that violent cataclysms such as blackhole collisions will cause the fabric of space itself to vibrate.

By the time they reach the earth, these ripples are so faint that picking themout of the surrounding noise is comparable to noticing a single grain of sandadded to all the beaches of Long Island, N.Y.

Six ultraprecise interferometers have been built around the world to detect these signals. Three are in the U.S. and began scientific observations in May. But they are still struggling to reach the necessary sensitivity.

Overview/Gravitational-Wave Detectors

DETECTING A QUIVER SO MINUSCULE IS LIKE NOTICING THAT SATURNHAS MOVED CLOSER TO THE SUN BY THE WIDTH OF A HYDROGEN ATOM.


able consequence of his general theory ofrelativity. The attractive force we callgravity, Einstein famously postulated, oc-curs because massive bodies warp thefour-dimensional fabric of the universe.If a dense object moves violently, spaceshudders in response.

When a giant star, for example, ex-hausts its fuel, it can detonate in a flash asluminous as 10 billion suns—a superno-va. Astronomers believe that the star’souter layers are blown into space, whileits iron core implodes with enough forceto combine all its electrons and protonsinto neutrons and exotic particles. With-in minutes, a solid metal sphere as big asthe earth collapses into a neutron star lessthan 20 kilometers across. It is so densethat a teaspoonful of its surface wouldweigh nearly a billion tons. Scientists ex-pect that a somewhat lopsided superno-va would send out neutrinos and a burstof gravitational energy that would hit theearth several minutes before the flash ar-rived—time enough to alert convention-

al astronomers to train their telescopes onit. More important, details about thebirth of the neutron star could be ex-tracted from the gravitational signal eventhough the nascent object itself is tiny andswaddled in a blanket of fiery gas.

LIGO was designed to detect thedeath of neutron stars as well as theirbirth. Most stars orbit a mate, and occa-sionally both stars in a binary pair will gosupernova yet remain locked in mutualthrall. With each revolution, the two neu-tron stars lose a little energy as they in-duce wrinkles in the surrounding fabricof space. Their orbit thus tightens step bystep until they rip apart and merge, some-times creating a black hole. Near the endof their frenetic tango, the massive bod-ies whirl around each other hundreds oftimes a second, flapping the bedsheets ofspacetime around them. Radio pulses

from such binary systems offer the mostconvincing, if indirect, evidence so farthat gravitational waves actually exist.

But it is still anyone’s guess whetherthe Caltech and M.I.T. groups that op-erate LIGO for the NSF will be able to de-tect such waves directly. “The curiousthing about LIGO,” Collins says, “isthat, at least in its first instantiation, itcannot promise success.”

Spectral PhenomenaTHE PROBLEM IS NOT that gravita-tional waves are weak. “The energy ingravitational waves is amazingly huge,”says Gabriela I. González, a physicist atLouisiana State University. During the fi-nal minute that neutron stars spiral totheir death 65 million light-years fromthe earth, the gravitational pulse wouldbe so energetic that “if it arrived in the


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CONTROL ROOM of the LIGO Livingston Observatory was home away from home for Caltech physicist Szabolcs Márka during the 18-day trial run, which he managed. Despite the challenges, theteam was able to collect more than 70 hours of scientific data from all three U.S. interferometers at once.


BY THE END OF 2003, six new gravitational-wave detectors should be online:one each near the cities of Livingston, La.; Hannover, Germany; Pisa, Italy;and Tokyo; and two at Hanford, Wash. Although they vary in size, sensitivityand details, all work in more or less the same way (bottom right; see alsobox on page 94 for more details). Because these ultrasensitive devicespick up so much terrestrial noise, scientists will use computers toscan the raw output (below) for predicted gravitational-wavepatterns, such as the chirp, crash and ring emitted by two blackholes in the seconds before and after they collide.

LIGO SPONSOR: U.S.ARM LENGTH: 4 km at Livingston; 4 km and 2 km at HanfordPEAK SENSITIVITY: Threeparts in 1023 at 180 HzSTATUS: Observations began in May 2002COST: $530 million through 2007

TAMA 300 (NOT SHOWN)SPONSOR: JapanARM LENGTH: 300 mPEAK SENSITIVITY: Fiveparts in 1021 from 700 to 1,000 Hz STATUS: Preliminary obser-vations began in 2001COST: $10 million

GEO 600SPONSORS: U.K., GermanyARM LENGTH: 600 mPEAK SENSITIVITY: Eightparts in 1023 at 600 HzSTATUS: Observations tobegin in 2002COST: $10 million

VIRGOSPONSORS: Italy, FranceARM LENGTH: 3 kmPEAK SENSITIVITY: One partin 1022 at 500 HzSTATUS: Observations to begin in 2003COST: $66 million “Peak sensitivity” refers to design goals not yet achieved

PINPOINTING THE SOURCEAs a gravitational pulse sweeps throughthe earth, the same waveform (green) willhit each detector at a slightly differenttime, allowing astronomers to pinpoint thesource and eliminate other possiblecauses of the vibration.

GLOBAL GRAVITY OBSERVATORY

1FREQUENCYMODULATOR

Creates areference beam

LASER 2MODE CLEANERRemoves

laser instabilities

RINGDOWN

LIGO LIVINGSTON

GEO 600

VIRGO

LIGO HANFORD

MATCH WITHTEMPLATE, POSSIBLE MERGER

MATCH WITHTEMPLATE,POSSIBLE MERGER

MATCH WITHTEMPLATE,POSSIBLE MERGER

OFFLINE BECAUSEOF EARTHQUAKE ININDONESIA

MERGERINSPIRAL

WOBBLING BY ONE PART IN A TRILLION BILLIONA gravitational wave will expand the space between themirrors in LIGO Livingston’s west arm (5 and 6) and will pullthe mirrors in the south arm closer. The larger thearms, the bigger the change. By forcing thelaser light in each arm to make about 100round-trips before returning to the beamsplitter (4), LIGO performs almost aswell as if it had arms 400 kilometers long.

SOUTHEND MIRROR


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REDUCING NOISE 100-MILLIONFOLDInterferometers measure the distancebetween two mirrors with subatomicprecision. To keep seismic rumbles fromruining the measurement, the mirrors arehung on pendulums (right) that are in turnbolted to multilayered isolation stacks(below right). Magnetic coils monitor themirrors’ positions and force the laser beam tocancel itself out at the dark port (7).

4BEAMSPLITTER

6WEST ENDMIRROR

5WEST INNERMIRROR

SOUTHINNER MIRROR

4 KM

3RECYCLINGMIRROR

Holds light incavity, boostingeffective power

EFFECTIVE SIZEOF LIGO ARMS

SUSPENSION BLOCK

ELECTROMAGNETICACTUATORS

MIRROR

LASER

COIL

CARBON-STEEL PIANO WIRE

ELASTOMER-FILLED SPRING

RESONANTMASSES

SUPPORTPILLAR

7PHOTODIODE AT DARK PORTRecords the interference

pattern produced by the referencebeam and the two test beams

LIGO is designed to detectmirror movements as small

as 10–18 meter. Thatdimension is to a hydrogen

atom what the scale above is tothe diagonal length of Louisiana

(about 560 kilometers).


form of visible light, it would be brighterthan the full moon,” González says.

But unlike light, which deposits all itsenergy when it splats against matter,gravity passes ghostlike through solid ob-jects with only a tingle of interaction. Toa gravitational wave, the earth and every-thing on it are almost perfectly transpar-ent. So even the powerful signal from themerging neutron stars will wiggle the cen-ter point of each mirror by just a few at-tometers (10–18 meter), the sensitivitythat LIGO was designed to achieve.

As one arm of the observatory swells,

the other will shrink. The phase and thefrequency of the laser light inside the armswill shift in opposite directions. When thebeams from the two arms are superim-posed on a reference beam, they will beout of tune, and the wavering beats theygenerate can be decoded by computers toreveal the changing curvature of space-time inside the arms. In principle, the tech-nique, known as interferometry, can mea-sure changes in distance much smallerthan the wavelength of the infrared laserlight—indeed, much smaller than the nu-cleus of an atom [see box below].

Ambitious as LIGO’s sensitivity goalis, it leaves astronomers unimpressed.Neutron couplets are relatively rare; theirdeaths are spectacular but quick. Within65 million light-years, astronomers esti-mate, only one such merger occurs every10,000 years. “So although it is possiblethat we would see these waves,” Thornesays, “it is not highly probable.” He thinksit more likely that LIGO would pick upblack hole mergers, which are 100 timesmore powerful than the neutron star va-riety. But theorists are uncertain by a fac-tor of 1,000 how frequently these events

A Photon’s Journey through LIGO

Laser

Reference beam

West arm

South arm

Darkport

Beamsplitter

Recyclingmirror

Modecleaner

INTERFERENCE PATTERNWest arm

Test beam

ReferencebeamSouth arm

Beamsplitter

1 2 3 4 5 6

Darkport

Beats in intensity

TO UNDERSTAND HOW THE LIGO interferometer works, imagine theadventure of a photon as it passes through the instrument. (We will neglect some details for clarity.) The photon is created in asuitcase-size laser that is as powerful as 20,000 laser pointers. It isone of trillions of photons marching in lockstep in an infrared beam.

1Part of the beam takes a detour into a device that converts thelight into two reference beams, one of slightly higher frequency

than the main beam and one of slightly lower frequency. Thisfrequency modulator thus creates a benchmark against which thetest beam can be compared at the end of its journey. After thedetour, the beams recombine and pass through a quartz windowand into the first vacuum chamber. The builders took everyprecaution to prevent our photon from scattering out of its intendedpath. Vacuum pumps hold the air pressure below one trillionth of anatmosphere. The mirrors, as wide as dinner plates and 10centimeters thick, have been polished to an accuracy of better than16 atoms. And the thickness of reflective films coating the opticsvaries by no more than two atoms.

2The photon enters a loop formed by three mirrors arranged in anarrow triangle. This mode cleaner is a quality checkpoint: the

photon can move ahead only if its part of the beam has just theright shape and direction. Any light that is out of place or poorlyaimed is tossed out a porthole.

3The photon next zips through a half-silvered mirror, whichblocks most photons that try to head back toward the laser. By

trapping photons within the device, this mirror increases the powerof the light beam 16-fold or more. Almost 100-fold additionalamplification occurs in the instruments’ long arms so that the beaminside those arms reaches the power of 20 million laser pointers.

4At the beam splitter, the photon divides into identical twins.One stream of photons continues forward into the west arm.

The other stream is inverted, its peaks flipped to valleys, as it isreflected into the south arm. The two test beams fly through theinner mirrors and into steel tubes four kilometers long. But thefrequency-shifted reference beams are denied entry. They retracetheir steps toward the beam splitter and circulate among thecentral optics until photons from the test beams return.

5Meanwhile our photon and its inverted twin sail down the longarms to bounce off a mirror at each end. Although the atoms

on the mirror surface are vibrating with heat, their motion israndom and the beam hits trillions of atoms at once. On averagethe thermal vibrations nearly cancel out. The twin photons carombetween the inner and end mirrors inside their respective arms.They make about 100 round-trips before leaking through the innermirror and reuniting at the beam splitter, which sends themnorthward toward the dark port. Normally our photon and its alterego will be at opposite points in their oscillation. Crest will meettrough, and the two will annihilate each other. The dark port will remain dark.

6But if during the photons’ journey, a gravitational wave slicesthrough the apparatus, it will have curved space, lengthening

one arm and shortening the other. Crest meets crest, and the darkport will light up. What’s more, the reunited photons will combinewith the frequency-modulated reference beams. Like musical notesplayed slightly out of tune, the light will beat, growing dimmer andbrighter with the passage of the gravitational wave. Finally hitting aphotodiode, the photon is converted into a perceptible electronicsignal, the trace of a trembling spacetime. —W.W.G.


might occur within LIGO’s range. Theremay be 10 a year or only one a century.

Going out to 300 million light-yearswould improve the odds, but then a typ-ical event would change the relativelength of LIGO’s arms by only about onepart in 1022. Observers will have to waitfor version 2.0 of LIGO to detect such aminuscule quiver, which is comparable tonoticing that Saturn has moved closer tothe sun by the width of a hydrogen atom.

The Unquiet EarthAS IF THAT WERE not difficult enough,LIGO engineers must contend with thefact that mirrors wiggle for lots of reasonsthat have nothing to do with supernovae,neutron stars or black holes. Heat causesmolecules in the mirrors and the wires onwhich they hang to jostle randomly. Thisthermal noise can drown out gravitation-al waves whose frequencies lie between 50and 200 hertz. At higher frequencies, theinterferometer is overwhelmed by thequantum effect called shot noise, whichoccurs because the number of photonshitting its sensors varies from one instantto the next. “You could turn the laserpower up to boost the signal over thenoise,” explains Norna Robertson, one ofthe designers of the GEO instrument.“But if you put too much light in, it kicksthe mirrors around in random ways.”

At the moment, though, the biggestchallenge for LIGO is at low frequencies,where the earth is constantly in motion.“At 100 hertz, the ground moves up anddown by about 10–11 meter,” Raab says.“We want to see motions of 10–19 meter”because that is a 1022nd of the four-kilo-meter length of LIGO’s arms. “So we needto reduce seismic noise 100-millionfold.”

We put on goggles and shoe coversand head over to the high bay that con-tains the laser and most of the detector’ssensors. As he opens the door to the cav-ernous room, Raab lowers his voice tojust above a whisper. I try to tread gently.

Raab walks over to a steel vacuumchamber as big as an upended van. To getfrom the ground to the mirror inside, aseismic rumble must pass through a stackof devices designed to sap its energy: aone-meter slab of reinforced concrete,scissor jacks, air bearings, four layers of

thick custom-made springs, four heavysteel plates (each resonating at a differentfrequency) and, finally, a pendulum ofsteel piano wire. “We reduce seismicnoise by a factor of 100 in the pendulumsuspension and by another factor of amillion with the isolation stacks,” Raabnotes. Some ground movements, such aslunar tides, still must be fought with moreactive devices, such as computer-con-trolled electromagnets that push and pullon tiny magnets glued to the mirrors.

Yet sometimes dampening externalnoise 100-millionfold isn’t enough. “Justrecently there was a magnitude-sevenearthquake in Sumatra; that knocked usoffline,” Raab says. Strong winds have

pulled the Hanford interferometer out oflock as well.

Not all seismic noise is natural. RobertSchofield, a postdoc at the University ofOregon, has become the noise detectivefor LIGO. One evening he is sitting at acontrol station frowning at a chart of thelatest signals picked up by the detector.“Look at this peak,” he says. “Right hereat 2.3 hertz. I hadn’t noticed it before be-cause it is so narrow, but it accounts for20 percent of the noise getting into the in-terferometer.” Scanning over readoutsfrom a battery of seismometers that sur-round the observatory, he concludes thatthe noise is coming from near the 200East section of the Hanford Nuclear


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MARK COLES, director of LIGO’s Louisiana facility, is trying to deal with logging, traffic and othersources of noise that thwart his engineers’ efforts. “It may be that in the first few years we won’t beable to get all the way to full design sensitivity,” he says. “But it’s still a great project to work on.”


Reservation, the 1,400-square-kilometerradioactive waste depository that sur-rounds the LIGO Hanford site.

Schofield marches down the hall, grabsa seismometer and an oscilloscope andhauls them into a van. He drives several

miles farther into the reservation, thenpulls over and sets up his equipment. Wecan see the bright lights of some night op-eration in 200 East several miles away. Butwe can’t get any closer because the areacontains tanks of plutonium-laced waste,and it is protected by security forces withsubmachine guns. Schofield sets the seis-mometer to listen for almost five minutes.But it reveals no trace of the 2.3-hertznoise. “I think it must be a large piece ofrotating machinery doing some fiendishthing out there,” he tells co-workers later.

Fortunately, noise near two hertz is

not an immediate problem. LIGO, likethe other giant gravitational-wave obser-vatories nearing completion—GEO inGermany, TAMA in Tokyo and VIRGOnear Pisa, Italy—is tuned to listen forgravitational waves from only 40 to

about 3,000 hertz, coincidentally right inthe range of human hearing. In the con-trol room, LIGO operators have con-nected a speaker to sensors on the inter-ferometer; it plays what the device“hears.” A nearby supernova mightcome through as a burst of static. Thewail of dying neutron stars would startlow and sweep higher in an almost mu-sical chirp.

Noise usually hisses and pops, but oc-casionally some recognizable sound leaksin. “There is a periscope on the laser tablethat raises the beam up to the right

height,” Schofield explains. Various nois-es can shake the periscope, introducingsubtle Doppler shifts in the frequency oflight passing through it. “If someone istalking near that periscope,” he says, “youcan hear their voice on that speaker.”

So in addition to the seismographs,LIGO engineers have studded the facilitywith microphones and magnetometers, aswell as sensors that monitor temperature,pressure and wind. A stream of data fromabout 5,000 sensor channels gets record-ed simultaneously. The first thing that sci-entists would do if they thought they sawa gravitational wave is look for glitches ornoise that had leaked into the system.

On the last day of the test run, Gon-zález hands the director, Mark Coles, aplot of the interferometer output fromthat morning. It contains a bounce that

IF LIGO ACHIEVES the sensitivity for which it was designed, it willstill have only a middling chance of detecting gravitational waves.“But our strategy from the beginning has been to do this in twosteps,” says Caltech physicist Kip S. Thorne: first get the machinesworking and gain confidence in their reliability, then upgrade to advanced components that will virtually guarantee regularsignal detections.

Although the project’s leaders have not yet made a formalproposal, they know roughly what they want. “It’ll cost on the orderof $100 million, begin around 2006 and take about two years tocomplete,” says LIGO director Barry Barish. The laser will beboosted from 10 to 180 watts. Instead of single loops of steel wire,the optics will hang on silica ribbons attached to a three-stagependulum now being tested in the GEO 600 detector in Germany.And the 11-kilogram silica glass mirrors will be replaced with 30-kilogram sapphire crystals.

The changes will boost sensitivity by a factor of 20, Barishestimates. That will put the instrument, Thorne says, “into thedomain where, for the first time in history, humans will be seeinghuman-size objects behaving quantum-mechanically.”Researchers have devised so-called quantum nondemolitiontechniques that can make measurements twice as precise asnormally allowed by the Heisenberg indeterminacy principle. If it all works, “it will increase by 8,000 times the volume of space wecan search,” Barish says.

The Japanese have also designed a successor to their TAMA300-meter interferometer, although project manager YoshihideKozai says, “I am afraid it will be a few years before we obtain thefunds” to start construction. The Large-Scale CryogenicGravitational Wave Telescope would have three-kilometer armsbuilt deep underground in the Kamioka mine. Supercooled sapphiremirrors of 51 kilograms each would help it match the sensitivity ofLIGO II at frequencies below 40 hertz.

NASA and the European Space Agency are designing an evenmore ambitious gravitational-wave observatory called LISA. A trio oflaser-toting satellites to be launched in 2011 would form aninterferometer with arms five million kilometers long—better than10 times the distance from the earth to the moon. As they orbitedthe sun, the trio would hold their position relative to one anotherwith one-micron precision. LISA would be no more sensitive thanLIGO II, but it could sense gravitational waves of much lowerfrequency than any detector built on the quaking earth.

“The most likely thing LISA would see is the motion of extremelymassive black holes—from a million to billions of times the mass ofthe sun—orbiting each other in the center of very distant galaxies,”Thorne says. “The astronomers are all over themselves about LISA,”reports M.I.T.’s Rainer Weiss. “They know for sure they will seeevents.” But because its cost will probably exceed half a billiondollars, Weiss predicts that “it will be much tougher to get LISAthrough Congress even than it was to get LIGO approved.” —W.W.G.

Next-Generation Detectors

THEORISTS HAVE A VERY POOR TRACK RECORD FOR PREDICTING WHATWE WILL SEE WHEN A NEW WINDOW IS OPENED ON THE UNIVERSE.


looks like a real signal. It isn’t. “We justinvented a speedometer for the cattleguard on the entrance road,” she sayswith a laugh. As each axle of a passingtruck hits the horizontal rails, a rumble ap-pears in the gravitational-wave channel.

Spurious signals can also be rejectedby comparing data from two or more ob-servatories, Márka explains. “If bothLIGO sites see the same shape signalwithin a few milliseconds of each otherand so does GEO, which sits on a differ-ent continental plate and is connected toa different electrical grid, then it is very,very unlikely to be a fake signal fromsome common source of noise.”

Yet there is only so much they can doto overcome human-generated noise. Theproblem is especially bad at the Liv-ingston site. “We can see the trains that goby three times a day,” Coles says. “Wecan see the workers hauling trees. We cansee when traffic picks up at lunchtime.”During this test run, the Livingston in-strument was online just 62 percent of thetime, not including short blips. All threeLIGO interferometers were up simulta-neously for only 18 percent of the run.

“We know we have a problem withground noise at Livingston,” acknowl-edges Rainer Weiss, spokesperson for theLIGO Scientific Collaboration. “And itwill get worse still. Society creeps in onus.” Barry Barish, head of the project,says new active isolation stacks are beingdeveloped and will be installed next year.“I wish we didn’t have to do it,” Weisssays. “That was an engineering enhance-ment we had planned to add during theupgrade to LIGO II in 2006.” The up-grade will add at least $750,000 to the$365 million that NSF has spent so far onthe project and to the $165 million that ithas just allotted for the next five years.

Yet even when the systems are lockedand working, Weiss says, “we’re stillmiles away—a factor of 1,000 away—

from our design sensitivity. We’re hopingto get at least 10 times better by June. Butbeyond that I don’t know. There aremany things we can try.”

The uncertainty still troubles LIGO’sold critic, Ostriker: “I have always be-lieved that detecting gravitational waveswill provide us insights obtainable in no

other way. That said, I think that theLIGO program has been an egregiouswaste of funds—funds that could havebeen used for more productive science.”

But Thorne sees things differently.“Theorists have a very poor track recordfor predicting what we will see when anew window is opened on the universe,”he says. “Early radio telescopes discov-ered that the signals were much strongerthan theorists expected. That happened

again when the x-ray window opened inthe 1960s. And when we started lookingfor neutrinos arriving from the sun, wewere surprised by how few there were. Insome sense, opening the gravitationalwindow will give us a more radically dif-ferent view on the universe than thoseprevious advances did.” Ripples in space-time may shake up science yet.

W. Wayt Gibbs is senior writer.


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G LIGO’s main Web site is www.ligo.caltech.edu

Einstein’s Unfinished Symphony. Marcia Bartusiak. Joseph Henry Press, 2000.Laser Interferometric Gravitational Wave Detectors. Norna A. Robertson in Classical and QuantumGravity, Vol. 17, No. 15, pages R19–R40; August 7, 2000. Available at www.iop.org/Journals/CQGNew Physics and Astronomy with the New Gravitational-Wave Observatories. Scott A. Hughes et al. in Proceedings of the 2001 Snowmass Meeting. Available atwww.ligo.caltech.edu/docs/P/P010029-00.pdf


STRAIGHTER THAN THE SURFACE OF THE EARTH, the concrete tunnel that houses the west arm of theLIGO Livingston Observatory rises more than a meter off the ground on its four-kilometer run as theplanet curves beneath it. The tunnel houses an airtight steel pipe. Inside the pipe is a vacuum, andthrough the vacuum shines a beam of infrared light with the power of 20 million laser pointers.


plan B

A lthough cosmic inflation has acquired an aura ofinvincibility, alternative theories explaining theevolution of the universe continue to attractsome interest among cosmologists. The steadystate theory, which until the 1960s was widelyregarded as the main alternative to the big bang,

has been kept alive by a small band of proponents. The pre–bigbang theory, a reworking of inflation that has been motivatedby string theory, also turns some heads. But the most promis-ing and provocative alternative may be the varying-speed-of-light theory (VSL), which my colleagues and I have been de-veloping for several years. If nothing else, these dissenting viewsadd color and variety to cosmology. They also give expressionto a nagging doubt: Could the enthusiasm generated by infla-tion and its offshoots conceal a monstrous error?

Mainstream cosmological theories such as inflation arebased on a crucial assumption: that the speed of light and oth-er fundamental physical parameters have had the same valuesfor all time. (They are, after all, known as constants.) This as-sumption has forced cosmologists to adopt inflation and all itsfantastic implications. And sure enough, experiments show thatthe presumed constants are not aging dramatically. Yet re-searchers have probed their values only over the past billionyears or so. Postulating their constancy over the entire life of theuniverse involves a massive extrapolation. Could the presumedconstants actually change over time in a big bang universe, asdo its temperature and density?

Theorists find that some constants are more agreeable thanothers to giving up their status. For instance, the gravitationalconstant, G, and the electron’s charge, e, have often been sub-jected to this theoretical ordeal, causing little scandal or uproar.Indeed, from Paul Dirac’s groundbreaking work on varyingconstants in the 1930s to the latest string theories, dethroning

the constancy of G has been exquisitely fashionable. In contrast,the speed of light, c, has remained inviolate. The reason is clear:the constancy of c and its status as a universal speed limit are thefoundations of the theory of relativity. And relativity’s spell isso strong that the constancy of c is now woven into all the math-ematical tools available to the physicist. “Varying c” is not evena swear word; it is simply not present in the vocabulary of physics.

Yet it might behoove cosmologists to expand their vernacu-lar. At the heart of inflation is the so-called horizon problem ofbig bang cosmology, which stems from a simple fact: at any giv-en time, light—and hence any interaction—can have traveledonly a finite distance since the big bang. When the universe wasone year old, for example, light could have traveled just one light-

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BY JOÃO MAGUEIJO

TROUBLE ON THE HORIZONAt the stripling age of one year, the universe was subdivided into isolatedpockets, demarcated by “horizons” one light-year in radius (blue spheres).Today the horizon is about 15 billion light-years in radius (red sphere), so ittakes in zillions of these pockets. The odd thing is that despite their initialisolation, all the pockets look pretty much the same. Explaining thismysterious uniformity is the great success of the theory of inflation.


JOÃO MAGUEIJO is a lecturer in theoretical physics at Imperial Col-lege, London. His research interests have oscillated between theobservational and the “lunatic” (his word) aspects of cosmolo-gy, from analysis of the cosmic microwave background radiationto topological defects, quintessence and black holes. He is the au-thor of the forthcoming book Faster Than the Speed of Light(Perseus Publishing).

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year (roughly). The universe is therefore fragmented into hori-zons, which demarcate regions that cannot yet see one another.

The shortsightedness of the universe is enormously irritat-ing to cosmologists. It precludes explanations based on physicalinteractions for puzzles such as why the early universe was souniform. Within the framework of the standard big bang theo-ry, the uniformity can be explained only by fine-tuning the ini-tial conditions—essentially a recourse to metaphysics.

Inflation cunningly gets around this problem. Its key insightis that for a light wave in an expanding universe, the distancefrom the starting point is greater than the distance traveled. Thereason is that expansion keeps stretching the space already cov-ered. By analogy, consider a driver who travels at 60 kilometersan hour for one hour. The driver has covered 60 kilometers, butif the road itself has elongated in the meantime, the distance fromthe point of departure is greater than 60 kilometers. Inflationarytheory postulates that the early universe expanded so fast thatthe range of light was phenomenally large. Seemingly disjointedregions could thus have communicated with one another andreached a common temperature and density. When the infla-tionary expansion ended, these regions began to fall out of touch.

It does not take much thought to realize that the same thingcould have been achieved if light simply had traveled faster in theearly universe than it does today. Fast light could have stitchedtogether a patchwork of otherwise disconnected regions. Theseregions could then have homogenized themselves. As the speedof light slowed, those regions would have fallen out of contact.

This was the initial insight that led Andreas C. Albrecht,then at the University of California at Berkeley, John Barrow ofthe University of Cambridge and me to propose the VSL theo-ry. Contrary to popular belief, our motivation was not to annoythe proponents of inflation. (Indeed, Albrecht is one of the fa-thers of inflationary theory.) We felt that the successes andshortcomings of inflation would become clearer if an alterna-tive existed, no matter how crude.

Naturally, VSL requires rethinking the foundations and lan-guage of physics, and for this reason a number of implementa-tions are possible. What we first proposed was a reckless act ofextreme violence against relativity, albeit with the redeemingmerit of solving many puzzles besides the flatness problem. Forexample, our theory accounts for the minuscule yet nonzero val-ue of the cosmological constant in today’s universe. The rea-son is that the vacuum-energy density represented by the cos-mological constant depends very strongly on c. A suitable dropin c reduces the otherwise domineering vacuum energy to in-nocuous levels. In standard theories, on the other hand, the vac-uum energy cannot be diluted.

But our formulation is just one possibility, and the urge toreconcile VSL to relativity is motivating much ongoing work.The more cautious implementations of VSL pioneered by JohnMoffat of the University of Toronto and later by Ian T. Drum-mond of Cambridge are easier for relativity theorists to swal-low. It now appears that the constancy of c is not so essentialto relativity after all; the theory can be based on other postu-lates. Some have pointed out that if the universe is a three-di-mensional membrane in a higher-dimensional space, as stringtheory suggests, the apparent speed of light in our world couldvary while the truly fundamental c remains constant. It has alsobeen suggested that a varying speed of light may be part and par-cel of any consistent theory of quantum gravity.

Whether nature chose to inflate or to monkey with c canonly be decided by experiment. The VSL theory is currently farless developed than inflation, so it has yet to make firm predic-tions for the cosmic microwave background radiation. On theother hand, some experiments have indicated that the so-calledfine structure constant may not be constant. Varying c wouldexplain those findings.

It remains to be seen whether these observations will with-stand further scrutiny; meanwhile VSL remains a major theo-retical challenge. It distinguishes itself from inflation by plung-ing deeper into the roots of physics. For now, VSL is far frombeing mainstream. It is a foray into the wild.

Time Varying Speed of Light as a Solution to Cosmological Puzzles.Andreas Albrecht and João Magueijo in Physical Review D, Vol. 59, No. 4,Paper No. 043516; February 15, 1999. Preprint available atxxx.lanl.gov/abs/astro-ph/9811018 Big Bang Riddles and Their Revelations. João Magueijo and Kim Baskerville in Philosophical Transactions of the Royal Society A, Vol. 357, No. 1763, pages 3221–3236; December 15, 1999.xxx.lanl.gov/abs/astro-ph/9905393Lorentz Invariance with an Invariant Energy Scale. João Magueijo andLee Smolin in Physical Review Letters, Vol. 88, No. 19; April 26, 2002.

BROADENING THE HORIZONInflation is not the only answer to the horizon problem. Instead maybeconditions in the early universe allowed light to travel faster than itspresent speed—a billion times faster or more. Zippy light made for biggerpockets (blue sphere). As light slowed to its present speed, the horizonshrank (red sphere). As a result, we now see just a part of one of the initialpockets, so it is no longer a mystery why the universe looks so uniform.



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