Optical depth of the universe at radiation-dominated epochs

Abstract

If the universe were radiation-dominated at redshifts greater than about 100-1000, e.g., due to the presence of a small fraction of light particles in the dark matter, it would be optically thin in soft gamma-rays up to redshifts of 10,000. This is larger by an order of magnitude than for the matter-dominated universe. X-rays and gamma-rays produced by cosmological high-energy processes are thus potentially observable up to z of about 10,000. Analytical formulas are derived for the optical depths of radiation-dominated universe due to photoionization, Compton scattering, photon-matter pair production, photon-photon scattering, and photon-photon pair production, in interactions with the cosmic thermal background and baryonic matter.