Addendum to: Update on neutrino mixing in the early Universe

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Abstract
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 Delta N_nu^tot, constrained by the primordial Helium abundance Y_p measurement, and Delta N_nu^rho, constrained by a combination of CMB and primordial Deuterium data. Small deviations from standard BBN are suggested. Different non standard scenarios can be distinguished by a measurement of the difference Delta N_nu^f_nu=Delta N_nu^tot-Delta N_nu^rho. From the current data we estimate Delta N_nu^f_nu simeq -1.4^{+0.9}_{-1.4}, mildly disfavouring solutions with a low expansion rate, characterized by Delta N_nu^f_nu=0 and negative Delta N_nu^rho. Active-sterile neutrino mixing could be a viable explanation only for high values of Y_p gtrsim 0.24. The existence of large positive neutrino chemical potentials xi_i sim 0.05, implying Delta N_nu^rho simeq 0, would be a possible explanation of the data within the analyzed class of non standard BBN models. Interestingly it would also provide a way to evade the cosmological bounds for `class A 3+1' four neutrino mixing models. A scenario with a decaying sterile neutrino is also considered.

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