On the sign of the neutrino asymmetry induced by active-sterile neutrino oscillations in the early Universe

We deal with the problem of the final sign of the neutrino asymmetry generated by active-sterile neutrino oscillations in the Early Universe solving the full momentum dependent quantum kinetic equations. We study the parameter region 10−2 < ∼ |δm2|/eV 2 ≤ 103. For a large range of sin 2θ0 values the sign of the neutrino asymmetry is fixed and does not oscillate. For values of mixing parameters in the region 10−6 < ∼ sin 2θ0 < ∼ 3× 10−4 (eV/|δm2|), the neutrino asymmetry appears to undergo rapid oscillations during the period where the exponential growth occurs. Our numerical results indicate that the oscillations are able to change the neutrino asymmetry sign. The sensitivity of the solutions and in particular of the final sign of lepton number to small changes in the initial conditions depends whether the number of oscillations is high enough. It is however not possible to conclude whether this effect is induced by the presence of a numerical error or is an intrinsic feature. As the amplitude of the statistical fluctuations is much lower than the numerical error, our numerical analysis cannot demonstrate the possibility of a chaotical generation of lepton domains. In any case this possibility is confined to a special region in the space of mixing parameters and it cannot spoil the compatibility of the νμ ↔ νs solution to the neutrino atmospheric data obtained assuming a small mixing of the νs with an eV − τ neutrino.