Radiation energy density

If we think in terms of the particulate nature of light (wave-particle duality), the number of particles of light or other electi omagnetic radiation (photons) in a unit of frequency space constitutes a number density. The blackbody radiation curve in Fig. 1-1, a plot of radiation energy density p on the vertical axis as a function of frequency v on the horizontal axis, is essentially a plot of the number densities of light particles in small intervals of frequency space. 

Einstein defined the B coefficients in terms of radiation energy density, but following E. A. Milne it is more... 

The specific intensity is (c/47t)x the radiation energy density and all photons ever emitted are still here (in the absence of intergalactic absorption). Their energy is reduced by a factor of (1 + z), which is taken up by the dv factor in any energy interval Ivdv, leaving Iv unchanged. 

By integration of Eq (1.26) over all wavelengths X, we obtain the total radiation energy density per unit volume... 

It is convenient to write the total (radiation) energy density in terms of that in the CMB photons... 

Black body radiation - The radiation emitted by a perfect black body, i.e., a body which absorbs all radiation incident on it and reflects none. The wavelength dependence of the radiated energy density p (energy per unit volume per unit wavelength range) is given by the Planck formula... 

Even though we have obtained this result in the case of Bosons an analogous calculation for Fermions yields identical formulas. Notice that these results confirm our previous findings for the energy density expressed in Eqs. (2.27) and (2.35). Notice also that in order for Eq. (5.145) (e a A -case) to yield agreement with the black body radiation energy density (cf. Remark 2 on page 200) we must require z = 1 or /u, = 0 for photons. 

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