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2.3. Composition of the universe

It is important to stress that absolutely no progress in cosmology can be made until a relationship between rho and P is provided, say, in the form of the functions wi(a)s. This fact, in turn, brings to focus two issues which are not often adequately emphasized:

(i) If we assume that the source is made of normal laboratory matter, then the relationship between rho and P depends on our knowledge of how the equation of state for matter behaves at different energy scales. This information needs to be provided by atomic physics, nuclear physics and particle physics. Cosmological models can at best be only as accurate as the input physics about Tik is; any definitive assertion about the state of the universe is misplaced, if the knowledge about Tik which it is based on is itself speculative or non existent at the relevant energy scales. At present we have laboratory results testing the behaviour of matter up to about 100 GeV and hence we can, in principle, determine the equation of state for matter up to 100 GeV. By and large, the equation of state for normal matter in this domain can be taken to be that of an ideal fluid with rho giving the energy density and P giving the pressure; the relation between the two is of the form P = wrho with w = 0 for non relativistic matter and w = (1/3) for relativistic matter and radiation.

(ii) The situation becomes more complicated when we realize that it is entirely possible for the large scale universe to be dominated by matter whose presence is undetectable at laboratory scales. For example, large scale scalar fields dominated either by kinetic energy or nearly constant potential energy could exist in the universe and will not be easily detectable at laboratory scales. We see from (6) that such systems can have an equation of state of the form P = wrho with w = 1 (for kinetic energy dominated scalar field) or w = - 1 (for potential energy dominated scalar field). While the conservative procedure for doing cosmology would be to use only known forms of Tik on the right hand side of Einstein's equations, this has the drawback of preventing progress in our understanding of nature, since cosmology could possibly be the only testing ground for the existence of forms of Tik which are difficult to detect at laboratory scales.

Figure 1

Figure 1. Cosmic inventory of energy densities. See text for description. (Figure adapted from [46].)

One of the key issues in modern cosmology has to do with the conflict in principle between (i) and (ii) above. Suppose a model based on conventional equation of state, adequately tested in the laboratory, fails to account for a cosmological observation. Should one treat this as a failure of the cosmological model or as a signal from nature for the existence of a source Tik not seen at laboratory scales? There is no easy answer to this question and we will focus on many facets of this issue in the coming sections.

Figure 1 provides an inventory of the density contributed by different forms of matter in the universe. The x-axis is actually a combination Omega hn of Omega and the Hubble parameter h since different components are measured by different techniques. (Usually n = 1 or 2; numerical values are for h = 0.7.) The density parameter contributed today by visible, non relativistic, baryonic matter in the universe is about OmegaB approx (0.01 - 0.2) (marked by triangles in the figure; different estimates are from different sources; see for a sample of references [51, 52, 53, 54, 55, 56, 57, 58, 59, 60]). The density parameter due to radiation is about OmegaR approx 2 × 10-5 (marked by squares in the figure). Unfortunately, models for the universe with just these two constituents for the energy density are in violent disagreement with observations. It appears to be necessary to postulate the existence of:

So in addition to H0, at least four more free parameters are required to describe the background universe at low energies (say, below 50 GeV). These are OmegaB, OmegaR, OmegaDM and OmegaLambda describing the fraction of the critical density contributed by baryonic matter, radiation (including relativistic particles like e.g, massive neutrinos; marked by a cross in the figure), dark matter and cosmological constant respectively. The first two certainly exist; the existence of last two is probably suggested by observations and is definitely not contradicted by any observations. Of these, only OmegaR is well constrained and other quantities are plagued by both statistical and systematic errors in their measurements. The top two positions in the contribution to Omega are from cosmological constant and non baryonic dark matter. It is unfortunate that we do not have laboratory evidence for the existence of the first two dominant contributions to the energy density in the universe. (This feature alone could make most of the cosmological paradigm described in this review irrelevant at a future date!)

The simplest model for the universe is based on the assumption that each of the sources which populate the universe has a constant wi; then equation (20) becomes

Equation 22 (22)

where each of these species is identified by density parameter Omegai and the equation of state characterized by wi. The most familiar form of energy densities are those due to pressure-less matter with wi = 0 (that is, non relativistic matter with rest mass energy density rho c2 dominating over the kinetic energy density, rho v2/2) and radiation with wi = (1/3). Whenever any one component of energy density dominates over others, P appeq wrho and it follows from the equation (22) (taking k = 0, for simplicity) that

Equation 23 (23)

For example, rho propto a-4, a propto t1/2 if the source is relativistic and rho propto a-3, a propto t2/3 if the source is non-relativistic.

This result shows that the past evolution of the universe is characterized by two important epochs (see eg. [43, 44]): (i) The first is the radiation dominated epoch which occurs at redshifts greater than zeq approx (OmegaDM / OmegaR) approx 104. For z gtapprox zeq the energy density is dominated by hot relativistic matter and the universe is very well approximated as a k = 0 model with a(t) propto t1/2. (ii) The second phase occurs for z << zeq in which the universe is dominated by non relativistic matter and - in some cases - the cosmological constant. The form of a(t) in this phase depends on the relative values of OmegaDM and OmegaLambda. In the simplest case, with OmegaDM approx 1, OmegaLambda = 0, OmegaB << OmegaDM the expansion is a power law with a(t) propto t2/3. (When cosmological constant dominates over matter, a(t) grows exponentially.)

During all the epochs, the temperature of the radiation varies as T propto a-1. When the temperature falls below T approx 103 K, neutral atomic systems form in the universe and photons decouple from matter. In this scenario, a relic background of such photons with Planckian spectrum at some non-zero temperature will exist in the present day universe. The present theory is, however, unable to predict the value of T at t = t0; it is therefore a free parameter related OmegaR propto T40.

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