Primordial neutrino asymmetry evolution with full mean-field effects and collisions

Neutrino oscillations and mean-field effects considerably enrich the phenomenology of neutrino evolution in the early Universe. Taking into account these effects, most notably the neutrino self-interaction mean-field contribution, we revisit the problem of the evolution of primordial neutrino asymmetries including for the first time the complete expression for collisions, which describe scattering and annihilations with electrons/positrons and reactions among (anti)neutrinos. We show that a generalisation of the adiabatic transfer of averaged oscillations (ATAO) scheme, a numerical method previously developed without neutrino degeneracy and based on the large separation of time scales in this problem, is sufficient to reach the same accuracy as the full quantum kinetic equation integration, but is notably faster. This approximation highlights the physics of synchronous oscillations at play in the evolution of neutrino chemical potentials, especially in the particular case with only two-neutrino mixing. In particular, it allows to understand what controls the beginning and the amplitude of oscillations, but also why there is a subsequent regime of collective oscillations with larger frequencies. We also find that it is very important to use the full collision term instead of relying on damping-like approximations, in order not to overestimate how collisions reduce these synchronous oscillations. Finally we study qualitatively how mixing parameters affect the final neutrino configuration, and in particular we show that the CP-violating Dirac phase cannot substantially affect the final $N_{\rm eff}$ nor the final electronic (anti)-neutrino spectrum, and thus should not affect cosmological observables.