At the present time, the average mass density of normal (baryonic) matter in the

Question

At the present time, the average mass density of normal (baryonic) matter in the Universe is about 4 × 10?-31 gm/cm?3. The temperature of the Cosmic Microwave Background (CMB) is 2.725 K, and it is very nearly a perfect black body.

a) What is the energy density in the CMB (in erg/cm?3)?
b) If this energy density were converted into an equivalent mass density using E = mc?2, what would the equivalent mass density be (in gm/cm?3)?
c) How does this compare to the mass density of ordinary matter?
d) At the present time, do we need to include the CMB in determining the gravitational ?eld of the Universe?

Explanation / Answer

a. given CMB temperature T = 2.725 K
hence energy densoity = a*T^4
a = radiation constat = 7.5657*10^-15 erg cm^-3 K-4
hence
U = 4.1717*10^-13 erg/cm^3

b. now, E = mc^2
hence rho = E/c^2 = 4.6352*10^-28 g/cm^3

c. mass density of ordinary matter = 4*10^-31 g/cm^3
so the denstiy of Cosmic background radiation is around 100 times more than the density of the prdinary material

d. hence to make up for this discrepancy, we have to take into account CMB to calculate the gravitational field of the universe

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