Nonequilibrium neutrino statistical mechanics in the expanding Universe

We study neutrino decoupling in the early Universe (t~sec,T~MeV) by integrating the Boltzmann equations that govern the neutrino phase-space distribution functions. In particular, we compute the distortions in the νₑ and ν_μν_τ 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 μ and τ neutrinos at the highest neutrino momenta, and correspond to an increase in the energy density of νₑ's of about 1.2% and in the energy density of ν_μν_τ'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 μ and τ 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, ΔY1-2×10^-4.