THE OPTICAL DEPTH OF THE UNIVERSE AT RADIATION-DOMINATED EPOCHS

We find that if the universe were radiation-dominated at redshifts z ≳ 102-103, e.g., due to the presence of a small fraction of light particles in the dark matter, it would be optically thin in soft γ-rays up to redshifts of z ∼ 104. This is larger by an order of magnitude than for the matter-dominated universe. X-rays and γ-rays produced by cosmological high-energy processes are thus potentially observable up to z of ∼ 104. We derive analytical formulae 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.