Addendum to “Update on neutrino mixing in the early universe”

Abstract

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 $\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{\mathrm{tot}},$ constrained by the primordial helium abundance ${Y}_{p}$ measurement, and $\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{\ensuremath{\rho}},$ 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 $\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{{f}_{\ensuremath{\nu}}}=\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{\mathrm{tot}}\ensuremath{-}\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{\ensuremath{\rho}}.$ From the current data we estimate $\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{{f}_{\ensuremath{\nu}}}\ensuremath{\simeq}\ensuremath{-}{1.4}_{\ensuremath{-}1.4}^{+0.9},$ mildly disfavoring solutions with a low expansion rate, characterized by $\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{{f}_{\ensuremath{\nu}}}=0$ and negative $\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{\ensuremath{\rho}}.$ Active-sterile neutrino mixing could be a viable explanation only for high values of ${Y}_{p}\ensuremath{\gtrsim}0.24.$ The existence of large positive neutrino chemical potentials ${\ensuremath{\xi}}_{i}\ensuremath{\sim}0.05,$ implying $\ensuremath{\Delta}{N}_{\ensuremath{\nu}}^{\ensuremath{\rho}}\ensuremath{\simeq}0,$ 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.