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Dark Energy Dominates the Universe

Martin Kilbinger & Marco Hetterscheidt


What is the Universe Made of?

A few decades ago, cosmology was a very data-starved science with many speculating theories. But as we have entered a new era of powerful instruments, cosmologists are presented with high quality data: now we have the capability to actually test the theories. Recent measurements of the cosmic microwave background (CMB) combined with supernovae of type Ia, cosmic shear, and galaxy cluster abundances show that $70\,\%$ of the Universe consists of the so-called dark energy, and $26\,\%$ of cold dark matter. Ordinary baryonic matter, in the form of gas and stars, only makes up $4\,\%$. If these measurements and their interpretation are correct, our Universe is spatially flat, as predicted by inflationary models. Furthermore, the Universe is dominated by a mysterious dark energy, which causes the cosmic expansion to accelerate.

$\textstyle \parbox{12cm}{\includegraphics[width=12cm,height=8.6cm]{kuchen-html.eps}}$

The Curvature of the Universe

The geometry of the Universe is determined by its curvature which can be positive, negative or zero. In these cases, the Universe is called closed, open or flat, respectively. The curvature on the other hand is governed by the total matter and energy content. For the so-called critical density $\rho_{\rm cr}$, the Universe is flat. If the total density is larger (smaller) than the critical density, the Universe is closed (open).

The contents of the Universe can be expressed in units of $\rho_{\rm cr}$. One usually defines the cosmological parameters as: $\Omega_{\rm\Lambda}:=\rho_\Lambda/\rho_{\rm cr}$ (dark energy), $\Omega_{\rm m}:=\rho_{\rm m}/\rho_{\rm cr}$ (cold dark matter and baryons) and $\Omega_{\rm b}:=\rho_{\rm b}/\rho_{\rm cr}$ (baryonic matter).

The scale of the CMB fluctuations directly indicates the curvature of the Universe and therefore the total density $\Omega_{\rm m} + \Omega_\Lambda$.


History of Dark Energy

Dark energy started its long history in 1917 and was introduced by Albert Einstein. A constant (which he called $\Lambda$) was needed in his equations of General Relativity in order to allow for a static Universe. But shortly thereafter, when Hubble made his famous discovery of the expansion of the Universe, this constant $\Lambda$, now seeming an unnatural and superfluous admixture, was rejected, even by Einstein himself (although his often cited ``biggest blunder in my life'' most probably is a myth).

Later, when quantum theory was developed, it was realized that ``empty space'' was full of temporary (``virtual'') particles continually forming and destroying themselves. Physicists began to suspect that indeed the vacuum ought to have a dark form of energy, and that Einstein's $\Lambda$ could be interpreted as vacuum energy. But when they tried to estimate its value, they disagreed with observational limits by 120 orders of magnitude, making this the most erroneous estimate in physics ever.

$\Lambda$ was forgotten by most astronomers for nearly 70 years. Most interestingly, $\Lambda$ was unearthed in the 1990s in order to reconcile theory with observations. Nowadays it has become fashionable to call $\Lambda$ ``dark energy''.

What is Dark Energy?

As yet, no scientist can give the answer to this fundamental question. We do not know what the nature of dark energy is, and unveiling this mystery will most probably reveal new physics and even might shake modern particle physics to its very foundations. Nevertheless, we have considerable astronomical knowledge about the properties of dark energy:

Observational Evidence

Supernovae Type Ia

Changes in the cosmic expansion rate can be studied with the observed brightness-redshift relation of type Ia supernovae (SNe). With the recent measurements of these distant exploding stars, the existence of dark energy has begun to gain broader consideration. Type Ia SNe are currently the best candidates for standard candles. They have the advantage of having a high luminosity and thus can be seen at cosmic distances. As a class, type Ia SNe are not equally luminous, but one can calibrate them with nearby SNe according to their brightening and fading. Using type Ia SNe as standard candles to gauge the expansion of the Universe, observers have found that it is currently accelerating. A cosmic dark energy will cause the expansion of the Universe to speed up. The results are most sensitive to the difference between $\Omega_{\rm m}$ (which decelerates the expansion) and $\Omega_\Lambda$ (which accelerates the expansion).

$\textstyle \parbox{10cm}{\includegraphics[width=10cm, height=8.5cm,viewport=94 254 510 657, clip]{supernovaII.ps}}$

$\textstyle \parbox{12.5cm}{\small Shown is the effective luminosity of the SNIa...
...g Universe, indicating
the presence of a cosmological constant or dark energy.}$

CMB Anisotropies

The supernovae data alone is accurate enough to exclude a vanishing $\Lambda$ at high significance. But there is more evidence. A precise determination of cosmological parameters comes from the measurement of the cosmic microwave background (CMB).

$\textstyle \parbox{13cm}{\begin{center}\includegraphics[width=12.5cm]{wmap-allsky-black.ps}

$\textstyle \parbox{12.5cm}{\small All-sky map of the cosmic microwave backgroun...
...10^{-5}$, their size gives direct indication of the flatness of the Universe.

$\textstyle \parbox{11.2cm}{\includegraphics[width=11.2cm]{cl2.ps}}$

$\textstyle \parbox{12.5cm}{\small Angular power spectrum of the CMB anisotropie...
...e position of the first peak one infers that the
Universe has a flat geometry.}$

According to the Big Bang model, the early Universe consisted of a hot gas of baryons and radiation. In this plasma, sound waves were generated which created density and temperature fluctuations. $300000$ years after the Big Bang the temperature of the Universe cooled down to $T\approx 3000 \, \rm {K}$ so that the hitherto ionized Universe became neutral. The now freely streaming photons still have the temperature fluctuations imprinted. These photons are redshifted by the expansion of the Universe to today's temperature of $T = 2.725
{\rm K}$ and form the CMB. Measuring the angular scales and heights of the temperature fluctuations in the CMB, expressed by the so-called angular power spectrum, one can directly determine the overall curvature of the Universe. If the curvature is positive (negative) the scales appear larger (smaller) on the sky compared to a flat Universe. This will result in a shift of the first dominant peak in the power spectrum. For a flat Universe, the characteristic scale of density fluctuations is $\sim 1^\circ$, resulting in a power spectrum peak near $l\approx 200$.

The Picture Converges

A number of different, independent observations such as galaxy surveys or the determination of cluster abundances, together with measurements of the baryon density inferred from Big Bang Nucleosynthesis (BBN) indicate a low-density Universe with $\Omega_{\rm m} \approx 0.3$. This implies that only a third of the critical density is present in matter.

But from CMB experiments such as WMAP, we know that our Universe is flat and therefore has indeed the critical density. Thus, there must be a missing dark energy component $\Omega_\Lambda \approx 0.7$ to fill the gap, in agreement with the SNIa results.

$\textstyle \parbox{8.5cm}{\colorbox{white}{\includegraphics[width=8.5cm]{pk_fit.eps}}}$

$\textstyle \parbox{12.5cm}{\small The likelihood contours from the 2dF galaxy s...
...re the baryon fraction is only 4\%, the rest being dark matter.

$\textstyle \parbox{10.5cm}{
\includegraphics[width=10.5cm,height=12.5cm, viewport=51 60 533 692,clip]{supernova-good.ps}}}$

$\textstyle \parbox{11.5cm}{\small Shown are three independent measurements of t...
...und (CMB) converge nicely near $\Omega_\Lambda=0.7$\ and
$\Omega_{\rm m}=0.3$.}$

Equation-of-State Parameter

The equation-of-state parameter indicates the connection between the pressure $p$ and the density $\rho$ of dark energy, via the equation $p = w \rho \, c^2$. A pure cosmological constant requires $w=-1$, quintessence models typically have $w>-1$. Both possibilities are still compatible with observations.

$\textstyle \parbox{8cm}{\includegraphics[width=8cm]{tegmark-Omegam-w.ps}}$

$\textstyle \parbox{12.5cm}{\small
A substantial fraction of parameter space for...
...ergy $w$\ is already
ruled out by WMAP, the galaxy survey SDSS and supernovae.}$


With high-precision cosmological observations we are now able to deepen our understanding of the Universe. For the first time we know the composition and geometry of our Universe in great detail. Although there is still some skepticism, a standard model of cosmology has emerged and seems to be consistent with all observations. We have very strong indications for non-vanishing dark energy, and the accelerated present expansion of the Universe has been measured. But we still do not know the physical nature of dark energy, and no theoretical model has succeeded to explain it convincingly.

The mere existence of dark energy will open a window to new and unpredictable physics. It is only by astronomical experiments that we can hope to enlighten the dark energy mystery. We live in a very exciting time where fundamental changes in the understanding of our world might be just around the corner.


Subject Title Author(s) Year Link(s)
Cosmological Constant/Dark Energy * The Cosmological Constant S.M. Carroll, W.H. Press & E.L. Turner 1992 ADS
* The Cosmological Constant S. M. Carroll 2000 ADS, astro-ph/0004075
* Why is the Universe Accelerating? S.M. Carroll 2003 astro-ph/0310342
CMB physics * Cosmic Microwave Background Anisotropies W. Hu & S. Dodelson 2002 ADS, astro-ph/0110414
First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters D.N. Spergel et. al. 2003 ADS, astro-ph/0302209
Supernovae New Constraints on Omega_M, Omega_Lambda, and w from an Independent Set of Eleven High-Redshift Supernovae Observed with HST R.A. Knop et. al. 2003 ADS, astro-ph/0309368
Observational Evidence from Supernovae for an Accelerated Universe and a Cosmological Constant A.G. Riess et. al. 1998 ADS, astro-ph/9805201
Measurements of Omega and Lambda from 42 High-Redshift Supernovae S. Perlmutter et. al. 1999 ADS, astro-ph/9812133
Galaxy Clusters * Clusters and Cosmology N. Bahcall 2000 ADS
Cosmological constraints from the X-ray gas mass fraction in relaxed lensing clusters observed with Chandra S.W. Allen, R.W. Schmidt & A.C. Fabian 2002 ADS, astro-ph/0205007
Galaxy Surveys Cosmological parameters from SDSS and WMAP M. Tegmark et. al. 2003 astro-ph/0310723

A * indicates a review paper.

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Martin Kilbinger & Marco Hetterscheidt () 12/2003