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

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 nu_s.Previous 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.