Primordial black holes evaporating before Big Bang nucleosynthesis

Abstract Primordial black holes (PBHs) formed from the collapse of density fluctuations provide a unique window into the physics of the early Universe. Their evaporation through Hawking radiation around the epoch of Big Bang nucleosynthesis (BBN) can leave measurable imprints on the primordial light-element abundances. In this work, we analyze in detail the effects of PBHs evaporating before BBN, with various intermediate steps understood analytically, and obtain the BBN constraint on PBHs within a transparent and reproducible framework. We find that, to produce observable effects on BBN, the PBH mass must exceed 10 9 g, a threshold higher than that reported in some earlier studies. Slightly above 10 9 g, the BBN sensitivity rapidly increases with the mass and then decreases, with the turning point occurring at 2×10 9 g. For PBHs in the mass range [10 9 , 10 10 ] g, current measurements of BBN observables set an upper bound on the initial mass fraction parameter β ranging from 10 -17 to 10 -19 . To facilitate future improvements, we make our code publicly available, enabling straightforward incorporation of updated nuclear reaction rates, particle-physics inputs, and cosmological data https://github.com/Fenyutanchan/Primordial-Black-Hole.git .