Neutrino Emission and Plasma Heating from Primordial Black Holes: An Improved Approach to $N_\mathrm{eff}$ Constraints

TL;DR

This paper refines constraints on primordial black holes by analyzing their neutrino emission effects on cosmological parameters, incorporating secondary neutrino production and plasma heating, leading to updated bounds on PBH abundance.

Contribution

It introduces a more comprehensive approach to constraining primordial black holes by including secondary neutrino emission and plasma heating effects in $N_{\mathrm{eff}}$ calculations.

Findings

Constraints on PBHs with masses $10^9$ to $10^{13}$ g.

Secondary neutrino emission increases $N_{\mathrm{eff}}$.

Plasma heating effects decrease $N_{\mathrm{eff}}$.

Abstract

We investigate the impact of neutrino emission via Hawking radiation from primordial black holes (PBHs) on the cosmological effective number of neutrino species, $N_{\mathrm{eff}}$, after neutrino decoupling. By comparing this effect with observational limits, we derive bounds on the abundance of light PBHs. Our analysis incorporates two previously unaccounted-for effects: the emission of secondary neutrinos from unstable particles, which increases $N_{\mathrm{eff}}$, and the modification of the neutrino-photon temperature ratio due to particle emission heating the photon plasma, which lowers $N_{\mathrm{eff}}$. Overall, including these effects allows us to impose constraints on PBHs with initial masses in the range $10^9~{\rm g}\lesssim M_{\rm ini} \lesssim 10^{13}~{\rm g}$. However, our limits remain less stringent than those derived from Big Bang Nucleosynthesis.