Updated BBN bounds on the cosmological lepton asymmetry for non-zero θ13

We discuss the bounds on the cosmological lepton number from Big Bang Nucleosynthesis (BBN), in light of recent evidences for a large value of the neutrino mixing angle θ13, sin2θ13≳0.01 at 2σ. The largest asymmetries for electron and μ, τ neutrinos compatible with He4 and H2 primordial yields are computed versus the neutrino mass hierarchy and mixing angles. The flavour oscillation dynamics is traced till the beginning of BBN and neutrino distributions after decoupling are numerically computed. The latter contains in general, non-thermal distortion due to the onset of flavour oscillations driven by solar squared mass difference in the temperature range where neutrino scatterings become inefficient to enforce thermodynamical equilibrium. Depending on the value of θ13, this translates into a larger value for the effective number of neutrinos, Neff. Upper bounds on this parameter are discussed for both neutrino mass hierarchies. Values for Neff which are large enough to be detectable by the Planck experiment are found only for the (presently disfavoured) range sin2θ13⩽0.01.