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 nonstandard big bang nucleosynthesis (BBN) models with a simultaneous combination of nonstandard neutrino distributions and an extra effective number of neutrinos in the expansion rate. These models can be described in terms of the two parameters $\Delta N_{\nu }^{\mathrm{tot}},$ constrained by the primordial helium abundance $Y_p$ measurement, and $\Delta N_{\nu }^{\rho },$ constrained by a combination of cosmic microwave background and primordial deuterium data. Small deviations from standard big bang nucleosynthesis are suggested. Different nonstandard scenarios can be distinguished by a measurement of the difference $\Delta N_{\nu }^{f_{\nu }}=\Delta N_{\nu }^{\mathrm{tot}}-\Delta N_{\nu }^{\rho }.$ From the current data we estimate $\Delta N_{\nu }^{f_{\nu }}\simeq -{1.4}_{-1.4}^{+0.9\mathrm{}},$ mildly disfavoring solutions with a low expansion rate, characterized by $\Delta N_{\nu }^{f_{\nu }}=0\mathrm{}$ and negative $\Delta N_{\nu }^{\rho }.$ Active-sterile neutrino mixing could be a viable explanation only for high values of $Y_p\gtrsim \mathrm{0.24.}$ 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 nonstandard 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.