Effect of neutrino heating in the early Universe on neutrino decoupling temperatures and nucleosynthesis

The neutrino energy-loss rates during pair annihilation in the early Universe are calculated using the formulation of Herrera and Hacyan and assuming neutrinos to be massless. The work is extended to include the neutrinos of the muon and tauon families, and a method to calculate the evolution of neutrino temperatures is suggested. It is found that neutrinos of the electron family decouple at 1.5×${10}^{10}$ K, and those of the other families at 2.5×${10}^{10}$ K. The former component is heated by about 0.36%, resulting in a reduction of the primordial abundance by a mass fraction of helium ($Y_p$) in the standard hot big-bang model by about 0.003.