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 PBH masses 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.