Nonequilibrium neutrino statistical mechanics in the expanding Universe

We study neutrino decoupling in the early Universe (t, T) by integrating the Boltzmann equations that govern the neutrino phase-space distribution functions. In particular, we compute the distortions in the ₄ and {_}{_} phase-space distributions that arise in the standard cosmology due to e^ annihilations. These distortions are nonthermal, with the effective neutrino temperature increasing with neutrino momentum, approaching a 0. 7% increase for electron neutrinos and a 0. 3% increase for and neutrinos at the highest neutrino momenta, and correspond to an increase in the energy density of ₄'s of about 1. 2% and in the energy density of {_}{_'s} of about 0. 5% (roughly one additional relic neutrino per cm^-3 per species). The distortion for electron neutrinos is larger than that for and neutrinos because electron neutrinos couple to e^'s through both charged- and neutral-current interactions. Our results graphically illustrate that neutrino decoupling is a continuous process which is momentum dependent. Because of subtle cancellations, these distortions lead to only a tiny change in the predicted primordial ^4He abundance, 1-210^-4.