Neutrino decoupling in the early Universe

Abstract

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 ${\mathit{e}}^{\ifmmode\pm\else\textpm\fi{}}$ annihilation. The corresponding number for \ensuremath{\mu} and \ensuremath{\tau} neutrinos is 0.41%. This has the consequence of modifying the primordial $^{4}\mathrm{He}$ abundance by \ensuremath{\Delta}Y=+1.0\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$, and the cosmological mass limit on light neutrinos by 0.2--0.5 eV.