BBN with electron-sterile neutrino oscillations — the finest leptometer

A relic lepton asymmetry orders of magnitude bigger than the baryon one may hide in the relic neutrino background. No direct theoretical or experimental limitations on its magnitude and sign are known. Only indirect cosmological constraints exist ranging from |L| < 0.01 to L < 10. Here we discuss a Big Bang Nucleosynthesis (BBN) model with late electron-sterile neutrino oscillations. The influence of L on neutrino oscillations and on nucleons freezing in the pre-BBN epoch is numerically analyzed in the full range of the oscillation parameters of the model and for |L| ≥ 10−10. The asymmetry-oscillations interplay is studied in detail and the behavior of L for different oscillation parameters is found. L effect on the primordially produced 4He is precisely studied. It is shown that this BBN model is a fine leptometer, capable of feeling extremely small relic lepton asymmetry — |L| > 10−8. The case of oscillations generated asymmetry by late electron-sterile oscillations and its effect on the primordial 4He is also briefly discussed. The instability region of the asymmetry growth is obtained