Numerical studies are performed for neutrino oscillations for t > 1/3
seconds after the big bang. The effects of electron, positron and neut
rino backgrounds are properly included. Flavor evolution of the neutri
no background is dominantly smooth. However, in a certain parameter re
gion, coherent undamped oscillations of the neutrino background are po
ssible. In addition, neutrino CP asymmetry is found to be considerably
smaller than expected. Reasons are provided for the above effects and
some physical implications are discussed.