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

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 $10^9\mathrm{g}\lesssim M_{\mathrm{ini}}\lesssim 10^{13}\mathrm{g}$. However, our limits remain less stringent than those derived from Big Bang Nucleosynthesis.

Comments: 26 pages, 4 figures. Major update. Changes: - Post-emission interactions of emitted unstable particles are now taken into account. - A more recent observational $N_{\mathrm{eff}}$ constraint is used for the bounds. - Various minor changes