1.1. Cosmic Densities

It is useful at this point to introduce the various densities, both observational and theoretical, which play a role in cosmology. They are given in any one of the following units. First the standard units: particle per cm³, g/cm³ or eV/cm³. Second, in units of temperature to the fourth power (T⁴) suggested by the fact that radiation energy density are expressed in these units. The following are useful numerical relations: the photon energy density is 4.5 × 10^-3(T⁴) eV/cm³, corresponding to 0.8 × 10^-35(T⁴) g/cm³. The T are in units of K.

The cosmic (2.7 K) background radiation, for instance, has an energy density of 0.24 eV/cm³ corresponding to (2.7 K)4. This corresponds to a mass density of 4.5 × 10^-34 g/cm³.

The critical density (needed to close the universe) is _c = 10^-29 g/cm³, (with H = 75), corresponding to a radiation density of (33 K)⁴. It is customary to define various densities in terms of a parameter / _c. Thus (fossil radiation) = 4.5 × 10^-5 (with a factor of two due to the uncertainty in the Hubble constant).

The density of luminous matter represents the matter which is detected through photon emission (i.e., nucleons and electrons). The conversion from the number density of light-emitting objects (average stellar luminosity per unit volume) to the corresponding matter density is not obvious. The standard unit for this conversion is the mass to luminosity ratio of the sun (M⁰ / L⁰ = 0.5 g/erg/sec). In this unit, the mean stellar population of a galaxy has an M/L ratio of 3 or so. Averaged over the galaxies, this corresponds to an (luminous) 0.003 (with an uncertainty of a factor of two).

The studies of the rotation curves of galaxies and of the stability of clusters of galaxies have revealed the presence of an extra component of matter which manifests itself through its gravitational field but does not emit photons. It is called dark matter. A better name would be clustered dark matter as it must be clustered either in galaxies or in clusters of galaxies. (We shall discuss later the possibility of an extra uniformly spread component which, by Gauss's theorem, could not affect the rotation curves or the stability of the cluster).

The present best estimate of (clustered) = 0.1, with an uncertainty of a factor of three each side.

We shall discuss in this chapter the determination of the baryonic density from primordial nucleosynthesis. Taking into account the uncertainties on the physics of the quark-hadron phase transition, we shall find that the data is best fitted by _b = 2 to 10 × 10^-31 g/cm³. This gives _b (baryonic) = 0.04 with a factor of three each side. The uncertainties of these two last determinations are seen to overlap. Thus the concentrated component may or may not be baryonic in nature.

Many theorists think that the universe should have exactly the critical density ( = 1). This appears to be required by the inflationary scenarios. Therefore they must postulate the existence of an extra component of dark matter (over and above the component needed to bind the clusters of galaxies). This component should not be baryonic nor should it be clustered in space as it would otherwise be in contradiction with the observations. In principle the existence of such an uniformly spread component could be tested by topological analysis of the space curvature. In practice this estimation is made exceedingly difficult by the fact that the expected effects are small unless one works on very large volume implying very distant galaxies. The uncertainties are usually too large for any reliable conclusions to be reached.

An upper limit to the cosmic density can nevertheless be obtained through the study of the deceleration of galaxies. Nearby galaxies should have experienced more gravitational deceleration than remote galaxies since they are observed at a later cosmological time. The lack of observed decelerations gives an upper limit of 3. This applies to all components of matter.

Aside from any theoretical argument, the best choice for the present density of the universe is (matter) = 0.1 (with a factor of three each side) a fair fraction of which being made of ordinary matter (nucleons and electrons). The baryonic number defined as the ratio of the number of nucleons over the number of photons is between 3 and 15 × 10^-10. Except during certain episodes, this number does not change with time. For this reason it will be most useful in our discussion.