Observational Background

Current observational data are driving cosmology in new and unexpected directions, leading to the quintessence hypothesis. This hypothesis rests on three basic pieces of evidence.

First, the energy density in matter which clusters is well below the critical energy density required to close the Universe: $\Omega_m < 1$. This result has been developing over a number of years [1]. One way to illustrate this result is to consider the mass-to-light ratio on increasingly large length scales. At the scale of clusters and superclusters, the largest objects in the Universe, the mass-to-light ratio appears to turn over, reaching a value near ${\rm M/L}\sim 200$ [14]. By Oort's method, the matter density is $\Omega_m = (M/L) \times (j/\rho_{crit})$ where $j$ is the observed luminosity density, obtaining $\Omega_m \sim 0.2 - 0.3$. Another method is to consider the baryon fraction in clusters, which is estimated to be $\Omega_b / \Omega_m \sim0.1 - 0.2$ [15]. Then using the Big Bang Nucleosynthesis constraint$\Omega_b h^2 = 0.02$ [16] we obtain a similarly low value, $\Omega_m\sim 0.2 - 0.5$ for reasonable values of the hubble parameter, $h$.

Figure 1: The conformal structure of the CMB is shown. The surface of the cone represents the flight path of photons traveling from the surface of last scattering. The dominant contribution to the temperature anisotropy is due to acoustic oscillations in the baryon-photon plasma on the scale of the sound horizon at recombination. Using the apparent size of this length scale in the CMB sky, the spatial curvature is determined to be small.

Second, the Universe is spatially flat. This has been argued on the basis of recent CMB results which show the presence of a sharp feature in the temperature anisotropy spectrum on the very angular scale predicted for a spatially flat Universe [17]. The way this works is straightforward. The predominant source of temperature anisotropy is through the Sachs-Wolfe effect, whereby photons climb out of deep gravitational potentials on the surface of last scattering, depicted in Figure 1. At recombination, the deepest and largest length-scale gravitational potential into which photons can fall is limited by the sound horizon. The consequence is a sharp peak in the anisotropy spectrum on the angular scale corresponding to the apparent size of the sound horizon at recombination. As a problem in geometric optics, the relation between the angular scale and the size of the sound horizon depends on the spatial curvature and distance to the last scattering surface. The prediction is that the peak should occur at a multipole$\ell \approx 220 / \sqrt{1-\Omega_k}$ where $\Omega_k$ is the spatial curvature expressed as a fraction of the critical energy density [18]. The location of the observed peak [3] as shown in Figure 2 strongly supports the claim of a spatially flat Universe, with$\vert\Omega_k\vert \ll 1$.
 

Figure 2: The angular power spectrum from COBE [19,20], Saskatoon [21], QMAP [22], TOCO97 [23], and TOCO98 ([3] from which this figure is taken) are shown. The rise and fall in the anisotropy spectrum in the range $\ell \sim 100 - 300$ in the TOCO98 data is the strongest evidence to date that the spatial curvature of the Universe is small. The cosmological models are SCDM (dashed line: $\Omega _m = 1$, $\Omega _{b} = 0.05$, $h=0.5$) and a $\Lambda$ concordance model [24] (solid line:$\Omega _m=0.33$, $\Omega _{b}=0.041$, $\Omega _\Lambda =0.67$, and $h=0.65$.) The error bars are $1\sigma$ statistical.
 

The first two pieces of information alone are enough to argue for the existence of an additional energy component. Examining the FRW equations, which can be rewritten as a sum rule for the fractional energy densities,

$${3 \over 8 \pi G} H^2 = -{k \over a^2} + \sum \rho_i \cr1$$

we see that $\Omega_m < 1$ and $\vert\Omega_k\vert \ll 1$ indicate that there must be some other term, $\Omega_{?}$, which brings the total up to unity. There must be some other component which dominates the total energy density today. But wait -- there's more.
 

 

Figure 3: The magnitude - red shift relationship traced by the type 1a supernovae measured by the SCP [6] and HZS [7] groups is shown. The vertical axis shows the magnitude difference with respect to an open, empty (accelerating) Universe, represented by the curve $\Delta (m-M)=0$. The top-most curve is the prediction for a $\Omega _\Lambda =1$ model; the bottom-most curve is for a $\Omega _m = 1$ model. The weight of the data strongly rules out the $\Omega _m = 1$ Universe, and favors models with $\Omega _m=0.3$ and $w=-1,\, -2/3,\, -1/3$ in decreasing order (the blue dashed, red dashed, and red dot-dashed curves).
 

Third, the cosmic expansion of the Universe is accelerating. This stunning claim is made on the basis of the magnitude - red shift relationship traced out by type 1a supernovae [6,7], as shown in Figure 3. The procedure can be summarized briefly. Although type 1a SNe are not standard candles, in that their intrinsic luminosity is not known, there appears to be an empirical relationship between the shape of the supernovae light curve and the luminosity. Hence, given the luminosity and the observed flux, the distance is determined; the red shift is determined by the host galaxy. The magnitude - red shift relationship then traces out an extended Hubble diagram, beyond the linear regime, which is sensitive to the cosmic acceleration. The evidence strongly favors a Universe in which the expansion is growing faster than that driven by pressureless dust. Since the acceleration of the expansion scale factor is

$${\ddot a} = -a {4 \pi G \over 3}( \rho + 3 p )$$

 
 

the observations demand negative pressure to be provided by an additional component.

Putting these three pieces of evidence together, the intersection indicates a low density, spatially flat, accelerating Universe.
The stage is set for the entrance of a dominant energy component with negative pressure.