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## Homework Statement

Reading about the raditation dominated era I saw that the radiation energy density today was given by:

[tex]

\rho_r = \frac{\pi^2}{30} g_* T^4 = 8.09 * 10^{-34} g/cm^3

[/tex]

where [itex]g_*=3.36[/itex] is the degree of freedom of the radiation (equivalent) and [itex]T=2.75 K[/itex] is the CBR temperature today.

The problem is that they dont give me the exact expression and so this relation seems to be dimensionally wrong. I suppose that the full relation must be

[tex]

\rho_r = \frac{\pi^2}{30} g_* \frac{(kT)^4}{(hc)^3}

[/tex]

and this way the relation would be dimensionally correct. But when I put the values on it I get

[tex]

\rho_r = 2.88 * 10^{-22} J/cm^3 = 3.20 * 10^{-36} g/cm^3

[/tex]

and this is by far wrong. I have spend so much time around this that I am starting to get frustrated!

Thanks in advance