A matter and radiation filled universe - Consequences of the astronomical observations

The Friedmann equations are solved for a universe containing matter and radiation in an arbitrary ratio without interaction between these two constituents. The consequences on the age of the Universe, the Hubble relation, the counting method, and the diameter of galaxies are derived with dependence on the cosmological parameter ..cap alpha..=1/..cap omega..=3H/sup 2//(8..pi..G/sub rho//sub 0/) and the matter parameter ..mu..=rho/sub 0/ /sub mat//rho/sub 0/(rho/sub 0/=rho/sub 0/ /sub mat/+rho/sub 0/ /sub rad/). ..mu..=rho/sub 0/ /sub mat//rho/sub 0/(rho/sub 0/=rho/sub 0/ /sub mat/ +rho/sub 0/ /sub rad/). In principle, both parameters ..cap alpha.. and ..mu.. can be determined by astronomical observations. (AIP)