Evolution of a primordial black hole population

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Abstract
We reconsider in this work the effects of an energy absorption term in the evolution of primordial black holes (PBHs) in several epochs of the Universe. A critical mass is introduced as a boundary between the accreting and evaporating regimes of the PBHs. We show that the growth of PBHs is negligible in the radiation-dominated era due to the scarcity of the energy density supply from the expanding background, in agreement with a previous analysis by Carr and Hawking, but that nevertheless the absorption term is large enough for black holes above the critical mass to preclude their evaporation until the universe has cooled sufficiently. The effects of PBH motion are also discussed: the Doppler effect may increase the energy accretion in black holes with large peculiar motions relative to background. We discuss how cosmological constraints are modified by the introduction of the critical mass since PBHs above it do not disturb the cosmic microwave background radiation. We show that there is a large range of admissible masses for PBHs above the critical mass, but well below the cosmological horizon. Finally we outline a minimal kinetic formalism, solved in some limiting cases, to deal with more complicated cases of PBH populations.
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