Addendum to: Update on neutrino mixing in the early Universe

In the light of the recent WMAP results we update the constraints on a class of non standard BBN models with a simultaneous combination of non standard neutrino distributions and extra effective number of neutrinos in the expansion rate. These models can be described in terms of the two parameters ∆N tot ν , constrained by the primordial Helium abundance Yp measurement, and ∆N ρ ν , constrained by a combination of CMB and primordial Deuterium data. Small deviations from standard Big Bang Nucleosynthesis are suggested. Different non standard scenarios can be distinguished by a measurement of the difference ∆N fν ν = ∆N tot ν − ∆N ρ ν . From the current data we estimate ∆N fν ν ≃ −1.4 +0.9 −1.4, slightly disfavouring solutions with a low expansion rate, characterized by ∆N fν ν = 0 and negative ∆N ρ ν . From the new WMAP upper bound on the abolute neutrino mass scale we show how active-sterile neutrino mixing could be still a viable explanation only for high values of Yp & 0.24, while it would be ruled out by low values Yp . 0.24. In this second case the existence of large positive neutrino chemical potentials ξi ∼ 0.05, implying ∆N ρ ν ≃ 0, would be a possible explanation of the data within the analyzed class of non standard BBN models.