Primordial Black Hole Evaporation and Dark Matter Production: I. Solely Hawking radiation

TL;DR

This paper refines calculations of dark matter production from primordial black holes via Hawking radiation, emphasizing the effects of particle spin, black hole rotation, and additional decay channels on relic abundance.

Contribution

It introduces improved models including greybody factors and coupled Boltzmann equations, revealing how black hole properties influence dark matter production.

Findings

Dark matter production varies by about two orders of magnitude with DM spin.

Kerr black holes enhance boson production, reducing initial density requirements.

Additional unstable particles can increase relic abundance by up to a factor of 4.

Abstract

Hawking evaporation of black holes in the early Universe is expected to copiously produce all kinds of particles, regardless of their charges under the Standard Model gauge group. For this reason, any fundamental particle, known or otherwise, could be produced during the black hole lifetime. This certainly includes dark matter (DM) particles. This paper improves upon previous calculations of DM production from primordial black holes (PBH) by consistently including the greybody factors, and by meticulously tracking a system of coupled Boltzmann equations. We show that the initial PBH densities required to produce the observed relic abundance depend strongly on the DM spin, varying in about $\sim 2$ orders of magnitude between a spin-2 and a scalar DM in the case of non-rotating PBHs. For Kerr PBHs, we have found that the expected enhancement in the production of bosons reduces the initial fraction needed to explain the measurements. We further consider indirect production of DM by assuming the existence of additional and unstable degrees of freedom emitted by the evaporation, which later decay into the DM. For a minimal setup where there is only one heavy particle, we find that the final relic abundance can be increased by at most a factor of $\sim 4$ for a scalar heavy state and a Schwarzschild PBH, or by a factor of $\sim 4.3$ for a spin-2 particle in the case of a Kerr PBH.