Neutrino emission and plasma heating from primordial black holes: an improved approach to N eff constraints

We investigate the impact of neutrino emission via Hawking radiation from primordial black holes (PBHs) on the cosmological effective number of neutrino species, N 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 eff , and the modification of the neutrino-photon temperature ratio due to particle emission heating the photon plasma, which lowers N eff . Overall, including these effects allows us to impose constraints on PBHs with initial masses in the range 10 9 g ≲ M ini ≲ 10 13 g. However, our limits remain less stringent than those derived from Big Bang Nucleosynthesis.