  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 $N_{\rm
eff}=3.0440$.
