matter and radiation in the early universe matter dominated universe (long after the epoch of "recombination") radiation dominated universe (long before the epoch of "recombinaiton") parameters proportionality (matter) where do these proportionalities come from  AND what constants or observations are needed to make the proportionality an equality? proportionality (radiation) what physics laws & what constants or observations are needed to make the proportionality an equality? density (matter or energy) as a function of "size" of universe ρ α r-3 definition of density; density now ρ α T4 x Temperature as function of the "size" of the universe T α r-1 x T α r-1 x "size" of the universe as a function of age of the universe r  α t2/3 x r α t1/2 x use the above to get: use the above to get: temperature-age dependence T α t-2/3 x T α t-1/2 x find the proportionality constant(s) to make the proportion an equality T/(3K) = [(13.7 x 109 yr)/t]2/3 T/(1.5 x 1010 K) = [(1 s)/t]1/2 does this match figure 26-11 (p. 703)? x x density-age dependence ρ α t-2 x ρ α t-2 x find the proportionality constant(s) to make the proportion an equality x x does this match match figure 26-10 (p. 702)? x x