Next Contents Previous

3.2.3 The current matter density of the universe rho0 and its normalized value Omega0

The matter density in space is of particular interest in relativistic universes, because it is closely related to the scale factor.

With the basic family of models introduced above (general relativity, Friedmann-Robertson-Walker metric) and the assumption Lambda = 0, and a presently matter dominated universe (p0 = 0), rho0 relates in simple ways scale factor, deceleration parameter and Riemannian space curvature.

Equation 32

Equation 33

The value of k is either +1, 0, -1 according to whether

Equation 34

It was from this formula, with k = 0, using the then accepted Hubble constant of 500 km sec-1 Mpc-1 that Einstein and de Sitter derived the value

rho0 = 4 x 10-28 g cm-3

in their famous paper of 1932.

Hubble (1934) determined the density of luminous matter in space from his counts of 44,000 nebulae with

log Mass = log b + 0.4 (5.7 - M)

with b = mass/luminosity ratio
M = absolute magnitude.

log b is estimated from nearby systems to be of order unity, M is estimated as -13.8 to -14.5. The result is given as

log rho0 = -29.8 or -29.9

with an uncertainty probably less than 0.5 (units of rho0 are g cm-3):

``The discussion, of course, ignores the existence of internebular matter, the density of which, even in an optimal form, might be several thousand times greater without introducing appreciable absorption. Since absorption depends upon the state of material (the density for large meteorites, for instance, might surpass that of the galactic system without introducing appreciable obscuration), upper limits can be assigned to the density of internebular space only from dynamical considerations.''

An earlier value (Hubble 1926) is

rho0 = 1.5 x 10-31 g cm-3.

The matter density rho0 is frequently replaced by the dimensionless quantity Omega0 which measures rho0 in terms of the Hubble constant, according to the above formula:

Equation 35

For Lambda = 0, Omega0 = 1, corresponding to the Euclidean universe (e.g. Borner 1988).

Omega0 can be determined directly from dynamical evidence, including the `cosmic virial theorem', and from the abundance of elements formed in the early universe.

Next Contents Previous