Neutrino decoupling in the early Universe

A calculation of neutrino decoupling in the early Universe, including full Fermi-Dirac statistics and electron mass dependence in the weak reaction rates, is presented. We find that after decoupling, the electron neutrinos contribute 0.83\% more to the relativistic energy density than in the standard scenario, where neutrinos are assumed not to share the heating from e$^\pm$ annihilation. The corresponding number for muon and tau neutrinos is 0.41\% . This has the consequence of modifying the primordial $^4$He abundance by $\Delta Y=+1.0\times 10^{-4}$, and the cosmological mass limit on light neutrinos by 0.2--0.5 eV.