Dark Energy: Origins and Evidence

ABSTRACT

The aim of this paper will be a review of the theoretical origins of the concept of Dark Energy in contemporary cosmology, tracing back its evolution from Einstein’s introduction of the cosmological constant λ in its field equations, through the observations of the CMBR and the observational confirmation of the acceleration of the expansion of the Universe in 1998 to more recent evidence for the existence of Dark Energy as drawn from observations of the Integrated Sachs-Wolfe Effect and models of the LSS of the universe. Some theories, including contributions from particle physics, around the nature of dark energy such as the quintessence hypothesis will be considered. Finally, future missions for the study of dark energy will be described.

EINSTEIN AND THE COSMOLOGICAL CONSTANT

In 1915, in an article titled Die Feldgleichungen der Gravitation (Einstein 1915) Alfred

Einstein published his field equations for general relativity (GR), thus completely

reconfiguring the field of physical cosmology by introducing a spacetime-based

understanding of gravity. Gravity, operating on large cosmic scales, became understood

as caused by matter and energy, hence a feature of space-time and not a force through

it. An implied consequence of his field equations was that the overarching presence of

matter would lead the universe towards a shrinking process caused by gravitational

attraction. Thus by 1917, envisioning a static universe (in harmony with the accepted

belief of the time), and wanting his model to be consistent with what he called the

‘Mach Principle’ (the principle for which the space-time metric should be fully

determined by the masses in the universe, and thus that the local dynamics were

conditioned by the universe at large) Einstein inserted a constant value in his field

equations, a ‘cosmological constant’, which would counteract the attractive action of

matter. Hence in his modified field equations,

the free parameter Λ1 now appears (we should note that it appears on the left side of

the equation referring to space-time not to matter-energy). When this modification of

GR was applied for an understanding of cosmological evolution the result was a so-

called ‘Einstein Static Universe’.2

This solution, however, didn't last long. In 1922 the Russian mathematician

Alexander Friedmann proposed a possible solution for the GR field equations that would

imply an expanding universe,3 and in 1927 the Belgian astronomer Georges Lemaître,

also criticized the Einsteinian idea of a possible static universe by proposing an

expanding universe as the solution favored by measurements (in fact predicting a

relationship between galaxies’ speed and their distance).4

By 1929 the Einsteinian static universe was finally observationally invalidated by

Edwin Hubble’s discoveries. Hubble, working with the 100-inch telescope on Mount

Wilson, discovered that the Milky Way was only one amongst many galaxies5 far away

from us and, by determining the outward velocities of these galaxies from the shift of

1 Einstein’s original notation was lower case lambda λ. In today’s notation the upper case one (Λ) is more commonly used.

2 Another important solution to Einstein’s field equations was Williem De Sitter’s one, which models the universe with no matter density, dominated by the cosmological constant and with a scale factor growing exponentially with time. Known as De Sitter Space this model is still largely used in cosmological theories.

3 Where he proposed the equation of ordinary cosmology ρ, which implies that as long as the

energy density ρ>0 the universe will expand. See Friedman 1922.4 See Lemaître 1927.5 Or, to be correct, in Hubble’s terminology nebulae.

visible spectral lines to longer wavelengths (redshift), he determined that those galaxies

were quickly receding from us, with a velocity that stands in direct proportion with their

distance (thus formulating—with Milton Humason—the Redshift Distance Law of

galaxies, nowadays simply termed Hubble's law).6 In Hubble’s words, it was observed

that there was a ‘roughly linear relation between velocities and distances among

nebulae for which velocities have been previously published, and the relation appears to

dominate the distribution of velocities’ (Hubble 1929: 173). This linear relation was

plotted in this way on a distance-velocity diagram:

Figure 1 – Hubble’s 1929 Distance-velocity diagram. From Hubble 1929.

Out of these observations the so-called Hubble law for a linear relation between

6 We must note that at Hubble’s time the technology only allowed for an observation of relatively close galaxies. Moreover, Hubble estimated distances using different kind of standard candles, mainly Cepheid Variables. As he explained: ‘The apparent luminosities of the brightest stars in such nebulae are thus criteria which, although rough and to be applied with caution, furnish reasonable estimates of the distances of all extra-galactic systems in which even a few stars can be detected’ (Hubble 1929: 168-169).

distance and velocity emerged:

v = H0 D

Where H0, the slope of the curve, represents the Hubble Constant, which was originally

calculated to hold a value of about 500 km/s/Mpc, but today is corrected7 to be circa

70.1 ± 1.3 km/s/Mpc. The general linear recession of far away objects from our

standpoint is commonly known as the Hubble Flow.

Einstein acknowledged the fact that this new evidence, by proving a dynamic and

expanding universe,8 made his introduction of a cosmological constant superfluous. He

thus eliminated it and famously described Λ as his ‘biggest blunder’. The cosmological

constant disappeared from the scene for several decades.

THE BIG BANG AND THE COSMIC MICROWAVE BACKRGOUND RADIATION

In the following decades, the standard consensus was therefore for an expanding

homogenous and isotropic universe according to the Friedmann-Lemaître metric.

According to Hubble’s law and the predictions of Lemaître, the age of the universe was

finite, and traceable simply by taking the inverse of the Hubble Constant 1/H0. Still, the

precise causal origin of the universe was still an object of debate, and different models

were proposed during the following years. While in the post-Second World War period

7 The specification of constraints for the Hubble constant has been influenced by new observational techniques and technologies: if around the 1960 the value dropped to about 100km/s/Mpc, only with the recent aid of fine-tuned observations made possible thanks to more technologically evolved probes such as the WMAP, the HST and the Chandra X-Ray Observatory the value has been corrected to the lower present figure. The Hubble constant represents one of the pillars of contemporary cosmology and the research for an ever-more-precise value of it is a crucial task for developing more precise cosmological theories.

8 As Kragh and Smith (2003) have shown, it is incorrect to claim that Hubble ‘discovered the expanding universe’. This point is often overlooked in common pedagogical renditions of the history of cosmology. Hubble observed a linear relation between redshift and distance for the light from far away nebulae/galaxies. He never directly postulated, from this data, the expansion of the universe. The expanding universe model was elaborated by theorists, mainly Friedmann and Lemaître, who used his data to corroborate their solutions for Einstein’s field equations.

cosmology was dominated by the clash between Fred Hoyle’s Steady State Theory and

the ‘Big Bang’9 Theory—prominently championed, amongst others, by George Gamow—

the final proof for an original Big Bang was given only in 1964,10 with the observational

discovery of Microwave Background Radiation.

Arno Penzias and James Wilson, working for Bell Laboratories on an antenna for

satellites communications, accidentally found a background noise signal, isotropically

spread around the sky, and soon realized that they had detected what Ralph Alpher and

Robert Herman had predicted11 (and George Gamow in 1948 before them) to be the

noise remnant of the original Big Bang ‘explosion’. This background noise, called the

Cosmic Microwave Background Radiation (CMBR) consistently fitted with the

predictions of the residual radiation from the Big Bang, with photons uniformly spread

around the universe. These photons have been redshifted to longer and longer

wavelengths (from the very high initial energetic states) by travelling so far after

decoupling (in the early stages of the formation of the universe), that they are today

observable to peak in the microwave part of their spectrum.12 Since its discovery, the

study of the CMBR has acquired a fundamental role in astronomy, for the great amount

of information it gives us about the origin and the evolution of the universe as a whole,

giving us a look-back time of about 380.000 years after the Big Bang. Several probes

have taken pictures of the sky in order to observe the CMBR, including the path-

breaking COBE (Cosmic Background Explorer) satellite, in the early 1990s and its higher-

definition successor the WMAP (Wilkinson Microwave Anisotropy Probe) satellite

launched into orbit in 2001 and still operational to this day.13

9 The name ‘Big Bang’ was actually coined by Fred Hoyle, in a BBC radio show in 1949, as a derogatory term for his adversaries’ theory. Originally the theory was known with no specific name, or occasionally as the ‘primeval atom’, with the term used by Lemaître.

10 As of today, we possess many other observations that can only be explained by the Big Bang, including the abundance of light elements form the Big Bang Nucleosynthesis in the observable universe and the spectroscopic observation of distant galaxies and quasars.

11 Ironically, Almer and Herman were still assembling the antenna necessary to prove their prediction when Penzias and Wilson randomly ‘bumped into’ it. As a matter of fact, the 1979 Nobel Prize for the CMBR went to Penzias and Wilson.

12 The spectrum of the CMBR peaks in the microwave range frequency of 160.2 GHz, corresponding to a 1.9 mm wavelength.

13 A new probe, the Plank Satellite, will be launched in spring 2009 and is expected to give even higher

Figure 2 – Comparison of the COBE and the WMAP CMBR pictures of the sky. The WMAP dramatic improvement in resolution (about 30 times the resolution of COBE) shows us in greater detail the anisotropies. From the NASA website http://www.nasa.gov/centers/goddard/news/topstory/2003/0206mapresults.html

The observations of the two satellites furnished final and incontrovertible proof

for the Big Bang, for the data gathered by them are perfectly consistent with a

blackbody radiation at the temperature of 2.752 K, and no other model than that of the

Big Bang can explain this exact observational value.

resolution measurements of the CMBR.

Figure 3 – The original graph presented in 1990 by John Mather (group leader, with George Smoot, of the COBE mission) at the American Astronomical Society meeting: the graph shows the concordance of the data points from the CMBR as observed by COBE and other probes and the radiation curve of a blackbody at 2.726 K.

However, as it is observable from the detailed WMAP pictures of the sky, the CMBR is

not perfectly isotropic. In fact, the measurements of these anisotropies gives us

precious information on the geometry of the Universe.

THE GEOMETRY OF THE UNIVERSE AND THE NECESSITY OF DARK ENERGY

The observations of the WMAP satellite led to a first theoretical need to postulate the

existence of a Dark Energy. We have seen above how Einstein’s theory General

Relativity establishes a fundamental relationship between matter and space-time (as

famously summarized by John Wheeler ‘matter tells space-time how to bend and space-

time tells matter how to move’). The curvature of space and the geometry of the

universe as a whole depends on the ratio between the total mass density of the

universe (matter and radiation, i.e. ρm + ρrad ) ρ0 and the critical density value ρc.14 This

14 The critical density is given by the equation ρc = , where G is the universal constant of gravitation.

ratio is known as Ω0 or density parameter.

Applying General Relativity, hence equilibrating the density of matter with its

gravitational potential, we find that Ω0 = 1 results in a flat universe never collapsing,

infinitely slowing down but never quite stopping, Ω0 > 1 implies a universe that will

eventually collapse and results in a closed universe and Ω0 < 1 suggest an eternal

expansion and it therefore results in an open universe.

Figure 4 – Graphic, bidimensional representations of the curvature of space according to the value of the density parameter Ω. Image retrieved at http://www4.nau.edu/meteorite/Meteorite/Book-GlossaryD.html

Figure 5 – Plotting the expansion of the universe as a curve according to the value of the density parameter Ω, with size as a function of time. The blue curve is for an open universe that expands forever, the green curve is for a flat universe that expands forever at an increasingly slower rate. The black and red curves are closed universes that recollapse on themselves: the higher the value of the density parameter, the quicker the recollapse. Graph retrieved at http://www.physics.carleton.ca/~watson/Physics/Astrophysics/CAP/CAP.html

The WMAP picture of the sky gives us hints about the geometry of space.15

Measuring the apparent size of the hottest microwave background fluctuations we are

in fact able to deduce the curvature of space: if the universe were open, the brightest of

those spots would be about half a degree across. If the universe were flat, they would

be about a degree across. If the universe were closed they would be about 1.5 degrees

across.16 The most accurate recent measurements tend to show spots of about 1 degree

across, hence suggesting a flat universe.17 This observation opens a gap in the

theoretical model. A flat universe, as we have seen, corresponds to Ω0=1, but Ωm, the

15 The same measurement was not possible before due to the poorer (about 7 degrees across) angular resolution of COBE. Other than the WMAP satellite, other missions that were instrumental for these measurements were the balloon-borne experiments MAXIMA (see Hanary et al 2000) and BOOMERANG (see De Bernardis et al 2000).

16 The variation in angular size are due to the curvature that the photons undergo in their travel from their source to our instruments. On large cosmic scales the sum of the interior angles of a triangle adds up to 180 degrees.

17 See Nolta et al. 2004.

matter density parameter ( ),18 equals to only 0.26. In other words, the total

density of matter in the universe (baryonic matter and unobserved Cold Dark Matter)

does not account for the unity of the density parameter: something other than matter

must be present to permit the observed existence of a flat universe, something not

detectable for its gravitational effects and that does not emit detectable radiation. Re-

employing Einstein’s parameter, astronomers identified this dark energy19 with Λ. The

new combined average mass density ρ0 must now be the sum of the average densities

of matter, radiation, and this new dark energy. Neglecting radiation we thus have:

ρ0 = ρm + ρΛ

Which divided by the critical density gives us:

Ω0 = Ωm + ΩΛ

so that

ΩΛ = Ω0 − Ωm

Where the result for ΩΛ is 0.74. This means that 74% of the Universe must be composed

by an unknown energy.

18 Where ρrad is neglected due to its small value.19 The paternity of the term ‘dark energy’ is generally attributed to Michael Turner who first employed

the term in Turner and Heuterer 1998.

Figure 6 – Pie chart of the expected composition of the universe. The values are indicative, being subject of constant refinement. Chart retrieved at http://map.gsfc.nasa.gov/media/060916/index.html

TYPE Ia SUPERNOVAE OF 1998 AND THE REINTRODUCTION OF Λ.

The only direct observational evidence for the acceleration of the cosmos—and

therefore an indirect proof for the existence of such an unknown dark energy—was

obtained in 1998, when two groups of astronomers (the Supernova Cosmology Project

at Lawrence Berkeley National Laboratory and the High-z Supernova Search Team),

made a new fundamental observational discovery (see Perlmutter et al. 1998 and Reiss

et al. 1998).

These groups gathered data from the bright explosions of Type Ia Supernovae:

this kind of supernova, being produced by the explosion of a white dwarf collapsing and

exploding when crossing the Chandrasekhar Limit20 after accretion of material from a

companion star, always produces a consistent peak luminosity21—due to the uniform

20 The Chandrasekhar limit is defined as being the maximum non-rotating mass which can be supported against gravitational collapse by electron degeneracy pressure. It is commonly given a value of 1.4 solar masses. If a collpsing’s star core is below this limit a white dwarf will form (i.e. no white dwarf normally exceeds 1.4 solar masses), if above this limit it will collapse to form a neutron star or a black hole.

21 Type Ia supernovae present a very characteristic and recognizable light curve and are defined by the

(and known) mass that triggers the explosion—thus acting as a very reliable standard

candle to measure astronomical distances. At the time, the starting assumption for

which confirmation was sought was that the universe was slowly decelerating due to

gravitational effects, eventually leading to a ‘big crunch’ or gravitational recollapse. The

data gathered by the groups, however, diverged greatly from the expected observation

of a slowing down of the expansion. The surprising discovery was indeed that the

recession speed of those supernovae (and thus of the galaxies which contained them)

was higher than the expected (as it would have been if purely due to the inertia from

the Big Bang) value. As the Hubble diagram below shows, the observed supernovae

seemed to be fainter (thus farther away) than expected according to a prediction based

on the basic cosmological model where Ω0=1, i.e., an expanding universe slowly

decelerating but ever so slowly.

feature of having no hydrogen lines in their spectra and to present a silicon absorption line at 6150 Å.

Figure 7 – Hubble diagram, of apparent magnitude versus redshift, for the data of the 1998 Supernova Cosmology Project. From Perlmutter et al. 1998.

In fact, the data seem to fit the curve of a flat universe whose expansion is accelerating,

where the distance/brightness curve acquires an ‘extra slope’ at higher redshifts. 22 This

means that the Hubble Constant, in fact, is not a constant23 but it has been varying with

time: theoretical models indicate that the universe started accelerating about 5 billion

years ago (that is, when dark energy’s effect overcame that of matter).

This discovery was considered a major breakthrough in the field,24 and gained

wide publicity within both specialized and more public-oriented publications,25 leading

to the picture of an ‘accelerating universe’. If in the previous decades, with the picture

of a post-inflationary universe expanding but slowly decelerating, there was no need for

Λ, this new picture or a universe accelerating its growth convinced astrophysicists to

look for some sort of gravitationally repulsive energy which isotropically permeates

space, to assume a Λ > 0, and hence to reconsider Einstein’s ‘blunder’.

In order to account for the observed acceleration of the universe, theorists had

to finally postulate the existence of a still unobserved energy, homogeneously

distributed throughout space and maintaining a constant density which does not

decrease with the expansion of space itself. Einstein’s cosmological constant seemed

the most obvious solution, since this energy must produce a repulsive force that

counteracts gravity and stretches the fabric of space-time, it must be homogeneously

spread around the universe and its density must be constant. This strange property

could be accounted by describing dark energy as a fluid which has a negative value. As in

22 Where redshift here is a measure of distance, being lower than z=1.46 where an object would be receding at superluminal velocity.

23 Today is in fact more correct to refer to it as the ‘Hubble parameter’.24 After 1998 more Type Ia Supernovae have been surveyed, trying to gather more precise data. The

latest published results from the Supernova Cosmology Project is Kowalski et al. 2008, and from the High-z Supernova Search Team is Reiss et al. 2007.

25 The December 1998 issue of Science Magazine titled on the cover The Accelerating Universe: Breakthrough of the year’ figuring a surprised Einstein observing expanding bubbles coming out of his pipe, when holding in hand its GR papers with Λ. See Glanz 1998.

the equation of state:

Ω = pΛ / ρΛ = -1

where pΛ is pressure of dark energy and ρΛ is density of dark energy. The negative

pressure would not influence the gravitational interaction of masses (it is incorrect to

talk about an ‘anti- gravitational’ effect) but it would modify the scale structure of the

universe at cosmological scales.

A consistent explanation of the nature or dark energy, however, is still lacking.

Among the possible options, particle physics theorists have suggested one is that dark

energy corresponds to a quantum level fluctuation known as zero-point energy, or

vacuum energy. This is a well known phenomenon, which can be experimentally

demonstrated (by the Casimir effect), where virtual particle-antiparticle pairs are

spontaneously generated in the vacuum only to immediately annihilate each other.

Unfortunately, the energy density of dark energy as deduced from observations is at a

factor of 10120 below the theoretical predictions of vacuum energy,26 a discrepancy yet

to be explained.

If quantum energy was responsible for the expansion of the universe, its

strength would have made impossible any sort of gravitational attraction and any

accretion of mass.27 The other main alternative explanation for dark energy is another

contribution from particle physics: a time-changing, gradually evolving scalar field,

2627 Linked to this, there is another still unexplained observation, known as the ‘coincidence problem’:

since the relative balance of vacuum and matter changes rapidly as the universe expands, it follows that at earlier times than now the vacuum energy was negligible in comparison to matter: it appears that we just happen to live in the epoch of the universe when it is possible to observe the vacuum energy starting to overtake the gravitational influence of matter. For a discussion on the theory-observation gap and on anthropic considerations on the coincidence problem see Weinberg 1989.

sometimes known as ‘quintessence’ which, differently from the cosmological constant,

is dynamic and varies both in density and equation of state through time and space.28

EVIDENCE FOR DARK ENERGY FROM ISW and LSS

Whatever the exact nature of dark energy is, a recent last set of observational evidence

seems to confirm its existence. The first set of these observations come from the

detection of the Late-Time Integrated Sachs-Wolfe effect (ISW) (see Sachs and Wolfe

1967) on very large scales structures (LSS) of the universe. Combining the

measurements of the CMBR by WMAP with spectrographic29 and X-Ray30 surveys of the

Large Scale Structures (LSS) of the universe (such as galaxy clusters and superclusters on

scales of about 100Mpc) astronomers have observed the ISW correlating the CMBR

anisotropies with the observed superclusters. When a photon from the CMBR passes

through a distant supercluster, which is loosely gravitationally bound, the photon would

normally gain some energy on the way in (gravitational blueshift) to then lose an equal

amount of energy on the way out of the gravitational well, leading to no net gain or loss

of energy. If the gravitational potential was increasing (due to gravitational attraction)

the photon would lose energy, and emerge redshifted, while if the gravitational

potential well was decaying (due to—we infer—dark energy) the photon would emerge

blueshifted. In ‘normal conditions’ we should observe no variation in temperature in the

CMBR when looking in the direction of that supercluster, but if the photon passing

through the gravitational potential had a net gain of energy (due to the effect of dark

energy) the region of space in the CMBR will look a bit hotter than the surrounding

region. The opposite will happen (a cooler region) if the photon was traversing a

supervoid region where there was no matter at all to counteract the stretching of space.

28 See Armendariz, Mukhaov & Steinhardt 2000 and Zlatev, Wang & Steinhardt 1999. Most quintessence models tend to do away with the cosmic coincidence problem by linking the formation of stars and planets able to host life and the transformation of quintessence into a negative pressure with the onset of matter domination in the universe.

29 As the Two Degree Field Galaxy Redshift Survey (2dF), or the Sloan Digital Sky Survey (SDSS).30 See Boughn et al. 2002.

This effect has been indeed recently observed (see Boughn & Crittemden 2004; Granett,

Neyrinck & Szapudi 2008).

Figure 8 – Fluctuations in temperature of the CMBR due to ISW. The differences are in order of a few microKelvin, but evident. From Granett Neyrinck & Szapudi 2008.

The second set of recent evidence also comes from mappings of the LSS of the

universe through X-ray or Weak Lensing observations. Our difficulty in detecting and

hence studying dark energy is that it is a force that, being homogeneously distributed

but extremely rarified (having a density of about 10-26 kg/m3), is hard to detect on small

scales. Employing the Chandra X-Ray observatory astronomers studied the formation

and evolution of huge structures of matter (superclusters) millions of light years across,

by observing the hot gas contained in these clusters both in extremely distant (older)

ones and in relatively closer ones. The measurements have shown how something is

preventing the clusters from merging as they would if only driven by gravitational

attraction: in other words, without dark energy, matter would keep clustering on ever

larger scales as the universe expanded but as dark energy eventually overcomes gravity,

metric expansion increases and the creation of new clusters (later times) interrupts:

according to the researchers this is proof of dark energy at work (see Vikhlinin et al.

2009 and Matson 2008).

Figure 9 – The two graphs plot the number of clusters as a function of their mass at two different redshift (z) angles (the higher the redshift, the farther the cluster). The left one assumes a Ω

Λ = 0.75, the right one

a ΩΛ = 0. The data points seem to have a better fit with the non-zero model. Graphs from Vikhlinin et al.

2009.

Figure 10 – The composite image on the left (X-ray and optical) shows the gas emissions from the galaxy cluster Abell 85, at about 740 million light years from Earth. On the right the illustration shows snapshots from a simulation by Vokler Springel representing the evolution of the matter structure of the universe, from left to right 0.9 billion, 3.2 billion and 17.7 billion (now) years from the Big Bang. Images retreived at http://chandra.harvard.edu/photo/2008/darkenergy/

Similarly, Weak Gravitational Lensing (WL) can be used for cosmological purposes and

gives us clues on the presence of dark energy through the measurement of mass

distribution and of evolution of structures. Gravitational deflection of light by

intervening (baryonic and dark) matter concentrations causes the images of background

galaxies to acquire a measurable additional ellipticity. This deformation (the cosmic

shear) effect associated with WL, caused by the differential deflection of neighboring

light rays, is very subtle (typically inducing an ellipticity of order 1%) and it requires high-

precision instruments in order not to be confused with image distortions due to

atmosphere and telescope optics, and therefore must be measured statistically using

the coherence of the lensing shear over the sky. Observations of lensed galaxies (at

known redshift) provide information on the matter distribution in the universe, as well

as the growth of density perturbations and the geometry of the universe itself. Since the

evolution of these galaxies and of the shapes of the large clusters they form is

dependent upon different values of dark energy and dark matter, this method is a

promising means to impose constraints on cosmological parameters.

Finally, another survey of LSS of the universe capable of giving us clues to the

presence of dark energy is the Baryon Oscillation Spectroscopic Survey (BOSS) part of

the Sloan Digital Sky Survey (SDSS). This survey studies galaxy distribution and density,

using as a standard ‘ruler’ the known 500 million light years cycle in which galaxies tend

bunch up together. By examining the variation in the density of matter, or Baryon

Acoustic Oscillations (BAO)—due to relic observable effect of sound waves in the

coupled baryon-photon pre-recombination plasma—in galaxy clusters up to z = 0.7, the

BOSS program can detect the angle of separation among galaxies and how much the

BAO has been influenced by dark matter since decoupling,31 some 300,000 years after

the Big Bang (see Percival et al. 2007 and Eisenstein et al. 2005).

The results of these surveys of the LSS are remarkably consistent with the SNe Ia

and the CMBR data, as the graph below clearly shows:

31 Since the CMBR gives us a perfect ‘snapshot’ of the universe precisely at the time of recombination, we can extrapolate the BAO ‘ruler’ from the CMBR itself. For a critique of this method see De Bernardis et al. 2008.

Figure 11 – Results from SNe, WMAP, Chandra X-ray observation of clusters and BAO plotted with ΩΛ (ΩX

in this graph) on the horizontal axis and the equation of state parameter w on the vertical. All the results seem to suggest values of W = -1 and Ω

Λ = 75%, hence supporting the cosmological constant option over

that of the quintessence. Graph from Vikhlinin et al. 2009.

OBSERVATIONS TO COME

As of today (2009) several missions are planned to obtain more precise observations

capable of giving us an account of the nature and action of dark matter in the universe,

and to prove (or disprove) the current ΛCDM model by finding new values for the basic

cosmological parameters.32

Among the most notable ones, the Joint Dark Energy Mission (JDEM) funded by

NASA and the US Department of Energy, scheduled in 2015, will employ the Supernova

Acceleration Probe (SNAP), designed as a survey telescope, to study thousands of high-

redshift supernovae from a redshift of 0.3 to 1.7 (both in visible and infrared) in order to

32 For the most recent constraints on the parameters of the ΛCDM model from the WMAP 5-year data see Komatsu et al. 2008.

gather more data on the universe’s growth. The observations possible with the 1.8

meter mirror orbiting probe will be extremely more accurate than ones with ground-

based telescopes (SNAP's resolution will be about 0.2 arcseconds in the visible and 0.3

arcseconds in the infrared)33 and part of its mission time will be will be employed to

measure WL as well.

Figure 12 – CG image of the SNAP orbital probe. The cutaway section shows the internal 1.8 meter mirror and the underlying CCD and NIR devices. From http://snap.lbl.gov/multimedia/images/.

Another promising future project, exclusively focused on dark energy-related

observations is the Dark Energy Survey (DES). This international project (universities

from the US, the UK and Spain are involved) will employ a high-resolution camera

mounted on the Blanco 4-meter telescope to take new large scale sky surveys. Thanks to

this instrument, the nature of dark energy will be probed with all the different known

techniques, including Cluster Counts, BAO, Supernovae detection and Weak Lensing.

DES is planned for construction starting in 2011.

33 See the SNAP website: http://snap.lbl.gov/.

Figure 13 – The camera and the Blanco telescope employed for the DES. From

http://www.darkenergysurvey.org/.

ESA’s planned Dark UNiverse Explorer (DUNE) will be a wide-field space imager

which will probe the LSS of the universe in search for evidence of dark energy. The

probe, carrying a 1.2 meters telescope with a field of vision of 0.5 degrees, will be

optimized for WL, but will also include BAO, galaxy clusters and the Integrated-Sachs

Wolf effect as complementary cosmological probes.

Figure 14 – The spacecraft platform hosting the DUNE telescope and Focal Plane Array. From http://www.dune-mission.net/.

Finally, for the study of the CMBR, ESA’s Plank Satellite will be sent in orbit in

April 2009 to reach the L2 lagrangian point of the Earth-Sun system where it will

measure anisotropies of the CMBR with highly improved definition and will allow for

best constraints to several cosmological parameters such as baryon density, matter

density, amplitude of primordial perturbations, temperature of the CMBR.

Figure 15 – The Plank satellite. From http://www.sciops.esa.int/index.php?

project=PLANCK&page=pictures_top

Future data gathered from all these projects (and others to come) will hopefully

be able to give us more information about the effects and the nature of dark energy,

and eventually allow us to consider its possible interactions with the other ‘parts’ of the

universe, baryonic matter and dark matter, and perhaps even to help us in resolving the

puzzle of the unification of quantum field theory with general relativity.

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Small Cosmological Constant and Late-time Cosmic Acceleration’, Phys.Rev.Lett., 85, pp. 4438-4441.

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