(Solved): 2. Using the appropriate form of the Friedmann equation for the early Universe (assuming kBT ...

2. Using the appropriate form of the Friedmann equation for the early Universe (assuming kBT < mec²), multiplying the energy density of the radiation background by a factor 1.68 to account for the contribution of neutrinos, and stating clearly any approximation used, show that the age of the Universe can be related to the photon temperature, T, via 3c² 3 t = T-2 = 1.8 x 1020T-2 sec, 32?1.68aBG where ag is the radiation density constant. Assuming that matter and radiation (including neutrinos) evolve independently, estimate the redshift at which they contribute equally to the total energy density.