Title:More General BBN Constraints on Neutrino Oscillations Parameters - Relaxed or Strengthened

Abstract: I discuss BBN with nonequilibrium nu_e<->nu_s oscillations in the more general case of non-zero population of nu_s before oscillations delta N_s>0. I calculate He-4 primordial production Y_p(delta N_s) in the presence of nu_e<->nu_s oscillations for different initial populations of nu_s state 0<=delta N_s<=1 and the full range of oscillation parameters.
Non-zero delta N_s has two-fold effect on He-4: (i) it enhances the energy density and hence increases the cosmic expansion rate, leading to Y_p overproduction and (ii) it suppresses the kinetic effects of oscillations on BBN, namely the effects on pre-BBN nucleon kinetics caused by the nu_e energy spectrum distortion and the neutrino-antineutrino asymmetry generation by oscillations, leading to decreased Y_p overproduction. Depending on oscillation parameters one or the other effect may dominate, causing, correspondingly, either a relaxation of the cosmological constraints or their strengthening with the increase of delta N_s .
I calculate more general BBN constraints on nu_e<->nu_s oscillation parameters,corresponding to 3% Y_p overproduction, for different initial populations of this http URL BBN constraints were derived assuming empty sterile state before oscillations. The cosmological constraints for that case strengthen with the increase of delta N_s value.