Precision calculation of neutrino evolution in the early Universe

In the primordial Universe, neutrino decoupling occurs only slightly before electron-positron annihilations. This leads notably to an increased neutrino energy density compared to the standard instantaneous decoupling approximation, parametrized by the effective number of neutrino species $N_{\rm eff}$. A precise calculation of neutrino evolution is needed to assess its consequences during the later cosmological stages, and requires to take into account multiple effects such as neutrino oscillations, which represents a genuine numerical challenge. Recently, several key improvements have allowed such a precise numerical calculation, leading to the new reference value $N_{\rm eff}=3.0440$.