BBN with Late 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. Indirect cosmological constraints exist ranging from $|L|<0.01$ to $L<10$. We discuss a BBN model with late electron-sterile neutrino oscillations which is a fine leptometer - it is capable of feeling extremely small relic lepton asymmetry - $|L|>10^{-8}$. This sensitivity is achieved through the influence of such small $L$ on the neutrino oscillations, suppressing or enhancing them, and thus changing the primordially produced $^4He$. The influence of $L$ on nucleons freezing in pre-BBN epoch is numerically analyzed in the full range of the oscillation parameters of the model and for $ L \ge 10^{-10}$. The case of oscillations generated asymmetry by late electron-sterile oscillations and its effect on primordial $^4He$ is also briefly discussed.