Science 3210 001 : Introduction to Astronomy

Lecture 12 : Cosmology

Robert Fisher

Items

Nathan Hearn guest lecture on dark matter today. Lunch in the loop (on me) with Nathan following the lecture at Frontera Fresco for anyone who wants to join us.

Adler Planetarium field trip on May 4th - $16/person -- to be collected next week. Waiver forms (Bob -- pick these up from 606!) to be signed!!

Final projects due May 11th, along with a short (5-10 minute) presentation that day.

Return midterms.

In the News This Week

Water discovered on HD209458b !!!

In memorium : Virginia Tech victims Liviu Librescu (1930 - 2007)

Final Project

Your final project is to construct a creative interpretation a scientific theme we encountered during the class. You will present your work in a five minute presentation in front of the entire class on May 11.

The project must have both a scientific component and a creative one.

For instance, a Jackson Pollock-lookalike painting would fly, but ONLY if you said that it was your interpretation of the big bang cosmological model AND you could also demonstrate mastery of the basic astrophysics of the big bang while presenting your work.

Be prepared to be grilled!

Ideas : Mount your camera on a tripod and shoot star trails. Create a “harmony of the worlds” soundtrack for the Upsilon Andromeda system. Paint the night sky as viewed from an observer about to fall behind the horizon of a

black hole. Write a short science fiction story about the discovery of intelligent life in the universe.

Two Weeks Ago

Michelson - Morley

Special Relativity

General Relativity

Last Week

Black Holes, White Holes, Wormholes

Galaxies Distances in the universe Types of galaxies

Ellipticals Spirals Irregulars

Today

Cosmology Why is the night sky dark? Newtonian Cosmology Einstein, Hubble and the Expansion of the Universe Cosmic Microwave Background

Large-Scale Structure of the Universe Clusters of Galaxies, Superclusters Quasars

Cosmology -- The Study of the Structure of the Universe as a Whole

Everyone has wondered about the “big” questions of cosmology Did the universe have a beginning? If so, how did it begin? Will the universe continue forever in time? Is the universe infinite or finite?

Every civilization has a “creation myth” which attempts to answer these questions

Modern science also seeks to answer these questions

In the last fifty years, tentative answers to these questions have begun to emerge, though they must still stand the rigors of science over time

Why is the Sky Dark at Night?

The modern study of cosmology began with a seemingly trivial but actually deep paradox. Why is the sky dark at night?

If the universe were infinite, and stars are uniformly distributed throughout space, we should see an infinite amount of luminous matter.

Not only would the night sky be bright, but it should be infinitely bright.

The fact fact that the night sky is in fact dark points to an apparent paradox.

The framing of the question is normally attributed to 19th century German astronomer Heinrich Olbers but was originally posed by Johannes Kepler some two hundred years previous.

Olbers Paradox is Like Viewing a Forest Full of Trees… if the Forest Were Infinite!

Question

What is wrong with Olbers’ argument?

Assumptions Underlying Olbers’ Paradox

Like most paradoxes, the night sky paradox makes a number of assumptions. Some of these are explicitly stated, others are implicit.

The universe is infinitely old and static (unchanging in time on average).

The universe is infinitely large.

Matter in the universe is uniformly distributed.

Like many paradoxes, it is the unstated assumption (that the universe is infinitely old) which we now know to be incorrect, and invalidates the argument.

Resolution to Olbers’ Paradox

If we throw out the assumption that the universe is infinitely old and static, then there is only a finite distance that light can travel in the age of the universe.

Hence, only a finite amount of matter is visible in a universe with a finite age.

The region of the universe visible to us is sometimes referred to as the cosmological horizon.

Speed of light x Age of Universe

Us

Physical Cosmology

One of the most important ideas which developed in modern astrophysics is that the structure of the universe as a whole can be understood using the fundamental principles of physics.

On the very largest scales, much larger than individual galaxies, gravity is the only force which is effective.

Large-Scale Structure

Physical Cosmology

When modeled as a physical system, astrophysicists often replace an amount of mass equivalent to an entire galaxy with a single body, or particle.

The entire assembly of particles is often referred to as an N-body system, particularly when simulated on a computer.

Millenium Simulation (Springel et al)

Newtonian Cosmology

The first serious attempt to formulate a fundamental scientific cosmological theory was due to Newton.

Newton envisioned an infinite universe, on an absolute, fixed space and time.

Newton’s gravity provided the prescription of how bodies moved within this space.

Each body in the universe is attracted by every other body under the influence of gravity and gravity alone.

Cambridge, We Have a Problem… Newtonian Cosmology is Totally Screwed Up

Unfortunately, it turns out to be completely impossible to formulate a consistent cosmological theory using Newtonian physics alone.

In Newtonian cosmology, because gravity propagates infinitely fast, if one clumps up matter in one place, the entire universe immediately feels the gravitational pull of that clump, and collapses in on it in a finite amount of time.

Cambridge, We Have a Problem… Newtonian Cosmology is Totally Screwed Up

Even if one seeded a bunch of clumps initially, these clumps would themselves coalesce on about the same time.

The lifespan of a Newtonian universe, based on the mean density of the intergalactic medium today, is about billion years.

Clearly the Newtonian model cannot account for the age of the Earth, much less detailed observations of the cosmos (eg, the Newtonian universe is collapsing!)

This model is fatally flawed, and it would take Einstein to fix that fatal flaw.

Einstein and Cosmology

In 1915, Einstein had formulated his theory of General Relativity (GR), which describes how gravity can be accounted for by the curvature of space and time under the influence of mass and energy within it.

It took until the end of WWI for Eddington to confirm GR using the bending of starlight during the 1917 solar eclipse.

With the successes of GR in our own solar system, Einstein turned to the same problem cosmological Newton had originally tackled -- what is the structure of the universe as a whole on very large scales?

Rare Photograph of Einstein Uncovered Recently

Einstein’s “Greatest Blunder”

Einstein began with similar building blocks as Newton, assuming that matter is smoothly distributed initially throughout space.

There is a fundamental difference between Newton’s model and Einstein’s. In Einstein’s model, space and time themselves are evolving as the universe evolves.

Einstein discovered that the matter within the universe would naturally create an expansion of space in relativity theory.

Taken at face value, Einstein’s original equations predict the expansion of the universe!!

Cosmological Constant

However, rather than accepting this description of an expanding universe (for which there was no direct evidence at the time), Einstein played with the equations to produce a static, unchanging universe similar in spirit to that originally proposed by Newton.

To produce this outcome, Einstein needed to add an additional term to his equations of General Relativity -- the so-called “cosmological constant” term, which is only important on very large scales.

The effect of the cosmological term is to counteract against gravity and produce an effective repulsion.

Hubble and the Expansion of the Universe

Working from Mt. Wilson Observatory near Pasadena, California, Edwin Hubble measured the distances to nearby galaxies using the Cepheid variable method pioneered by Henrietta Leavitt we discussed last week.

In addition, Hubble also measured the spectra of these galaxies.

Using the Doppler effect, he was able to determine the speed with which they receded from us from their spectra.

Amazingly, he found that the speed of recession was directly correlated with the distance to the galaxy.

Hubble’s Original Data, Showing Velocity Versus Distance for a Number of Galaxies

Slope of the line on this plot is the Hubble “constant”.

The Expansion of the Universe via Analogy

It turns out that the complex mathematics of GR in fact reduces to a very simple equation when describing the expansion of the universe -- the same one that are produced for a rocket moving at a fixed speed in a gravitational field in Newtonian physics.

VelocityGravity

The Expansion of the Universe

GR cosmology has a close correspondence in the rocket ship analogy. The height of the rocket is analogous the to radius of the universe, the strength of the gravitational field is analogous to the density of matter in the cosmos, and the speed of the rocket is analogous to the Hubble “constant” as it is measured today.

Curvature of Universe

Is the Universe Open, Closed, or Flat? Will it Collapse or Continue Expanding Forever?

While Hubble’s original Cepheid variable data clearly showed the expansion of the universe, the jury on the value of the Hubble constant was out for many years.

Hubble’s original value (500 km/s/Mpc) was much larger than the modern value (by a factor of 7) due to errors in the calibration of the Cepheids.

By the late 1980s, the uncertainty in the Hubble constant was down to a factor of 2. Enormous debates raged as to which value was correct, and whether the universe was open or closed.

A huge dedicated effort was undertaken by numerous groups to reduce this uncertainty even further and nail once and for all what the ultimate fate of the universe will be.

Modern Value of Hubble Constant

Fittingly, one of the major achievements of the Hubble Space Telescope and other parallel projects was the accurate determination of the Hubble constant, which is now known to better than 10%.

A Flat, Accelerating Universe

Observations of distant type Ia supernovae (which we discussed a few weeks ago) serve as excellent standard candles.

These observations are consistent with a flat, accelerating universe.

Einstein’s Greatest Blunder? Maybe Not.

What is causing the acceleration of the universe?

It is consistent with a cosmological constant.

Cosmic Microwave Background

Large-Scale Structure of the Universe

Zoom-in of Millenium Simulation

Flythrough of Large-Scale Structure of the Millenium Simulation

Next Week : Interstellar Space Travel, Life in the Universe, and the Ultimate Fate of the Universe

Does life exist elsewhere in the universe? How can science address this age-old question?

Does intelligent life exist elsewhere in the universe? How can we search for extraterrestrial intelligence?

Is it possible for humans to travel to other stars?

What is the ultimate fate of the universe?

Wrapping it all up -- from ancient astronomy to the infinite far future of the universe