NONEQUILIBRIUM NEUTRINO STATISTICAL-MECHANICS IN THE EXPANDING UNIVERSE

We study neutrino decoupling in the early Universe (t approximately sec, T approximately MeV) by integrating the Boltzmann equations that govern the neutrino phase-space distribution functions. In particular, we compute the distortions in the nu(e) and nu(mu)/nu(tau) 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 mu and tau neutrinos at the highest neutrino momenta, and correspond to an increase in the energy density of nu(e)'s of about 1.2% and in the energy density of nu(mu)/nu(tau)'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 mu and tau 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 He-4 abundance, DELTAY congruent-to 1-2 X 10(-4).