Incomplete neutrino decoupling effect on big bang nucleosynthesis

In the primordial Universe, neutrino decoupling occurs only slightly before electrons-positrons annihilations, leading to an increased neutrino energy density with order $10^{-2}$ spectral distortions compared to the standard instantaneous decoupling approximation. However, there are discrepancies in literature on the impact it has on the subsequent primordial nucleosynthesis, not only on the magnitude of the abundance modifications, but also on their sign. We review how neutrino decoupling affects indirectly the various stages of nucleosynthesis, namely the freezing out of neutron abundance, the duration of neutron beta decay, and the nucleosynthesis itself. This allows to predict the sign of abundance variations which are expected when the physics of neutrino decoupling is taken into account. For simplicity, we ignore neutrino oscillations, but we conjecture from the detailed interplay of neutrino temperature shifts and distortions that their effect on final light elements abundances should be subdominant.