CP violation effects on the neutrino degeneracy parameters in the Early Universe

Abstract: We explore possible CP violating effects, coming from the Dirac phase of the Maki-Nakagawa-Sakata-Pontecorvo matrix, on the neutrino degeneracy parameters, at the epoch of Big-Bang nucleosynthesis. We first demonstrate the conditions under which such effects can arise. In particular it requires that the initial muon and tau neutrino degeneracy parameters differ. Then we solve numerically the kinetic equations for the three flavour neutrino density matrix with the goal of quantifying the impact of the Dirac phase on the electron neutrino degeneracy parameter. The calculations include the vacuum term, the coupling to matter, the neutrino-neutrino interaction and the collisions. Effects on electron neutrino degeneracy parameter up to almost 1.% and on Yp of about 0.1% are found, depending on the initial conditions.