Sources of radiation in the early Universe: The equation of radiative transfer and optical distances

Abstract

We have derived the radiative-transfer equation for a point source with a specified intensity and spectrum, originating in the early Universe between the epochs of annihilation and recombination, at redshifts z _s = 10⁸∓10⁴. The direct radiation of the source is separated from the diffuse radiation it produces. Optical distances from the source for Thomson scattering and bremsstrahlung absorption at the maximum of the thermal background radiation are calculated as a function of the redshift z. The distances grow sharply with decreasing z, approaching asymptotic values, the absorption distance increasing more slowly and reaching their limiting values at lower z. For the adopted z values, the optical parameters of the Universe can be described in a flat model with dusty material and radiation, and radiative transfer can be treated in a grey approximation.