Here's the problem:
It is more common to define the “effective number of relativistic degrees of freedom” by writing the total radiation energy as ρR = ργ + ρν + ρe± = (π^2/30) g∗*T^4 , where g∗ = 2 + 7/8(6 + 4) = 43/4 . (1.52) With this, the expansion rate during the radiation era is given by...