Consistent Neff fitting in big bang nucleosynthesis analysis

The effective number of neutrino species, Neff, serves as a key fitting parameter extensively employed in cosmological studies. In this work, we point out a fundamental inconsistency in the conventional treatment of Neff in big bang nucleosynthesis (BBN), particularly regarding its applicability to new physics scenarios where ΔNeff, the deviation of Neff from the standard BBN prediction, is negative. To ensure consistent interpretation, it is imperative to either restrict the allowed range of Neff or systematically adjust neutrino-induced reaction rates based on physically motivated assumptions. As a concrete example, we consider a simple scenario in which a negative ΔNeff arises from entropy injection into the electromagnetic sector due to the decay of long-lived particles after neutrino decoupling. This process dilutes the neutrino density and suppresses the rate of neutrino-driven neutron-proton conversion. Under this assumption, we demonstrate that the resulting BBN constraints on Neff deviate significantly from those obtained by the conventional, but unphysical, extrapolation of dark radiation scenarios into the ΔNeff < 0 regime.