1.2. Reaching for the past
From the previous discussion we gather that the present universe is matter dominated. The matter density is some 2 × 103 larger than the radiation density ((fossil radiation) = 4.5 × 10-5 while (matter) = 0.1). However, as the energy density of a matter-dominated universe decreases with T3 - while the dependance is in T4 for a radiation dominated universe - we conclude that both densities were equal when the universe was some 2 × 103 times hotter, that is at approximately 5 × 103 K. The density was (2 × 103)3 larger. In these conditions the hydrogen atoms were ionized and the cosmic fluid was opaque to its own radiation. The fossil radiation observed by Penzias and Wilson is believed to have been emitted at the moment of recombination of hydrogen, approximately when the universe became matter-dominated.
To the question: how hot has the universe been in the past? we can give a first answer in the following way. As beautifully confirmed by the COBE satellite in march 90, the fossil radiation has, very accurately, a thermal (Bose-Einstein) distribution of photon momenta. In the present universe there are no known physical processes capable of thermalizing a population of photons. We need to go back to temperature of at least a few thousand degrees to find appropriate physical conditions. Thus we may conclude that the existence of the fossil radiation gives us strong indications that, in the past, the universe has reached such temperatures.