Constraints on neutrino degeneracy from the cosmic microwave background and primordial nucleosynthesis

Abstract

We reanalyze the cosmological constraints on the existence of a net universal lepton asymmetry and neutrino degeneracy based upon the latest high resolution CMB sky maps from BOOMERANG, DASI, and MAXIMA-1. We generate likelihood functions by marginalizing over $({\ensuremath{\Omega}}_{\mathrm{b}}{h}^{2},{\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\mu},\ensuremath{\tau}}},{\ensuremath{\xi}}_{{\ensuremath{\nu}}_{e}},{\ensuremath{\Omega}}_{\ensuremath{\Lambda}},h,n)$ plus the calibration uncertainties. We consider flat ${\ensuremath{\Omega}}_{M}+{\ensuremath{\Omega}}_{\ensuremath{\Lambda}}=1$ cosmological models with two identical degenerate neutrino species, ${\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\mu},\ensuremath{\tau}}}\ensuremath{\equiv}|{\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\mu}}}|=|{\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\tau}}}|$ and a small ${\ensuremath{\xi}}_{{\ensuremath{\nu}}_{e}}.$ We assign weak top-hat priors on the electron-neutrino degeneracy parameter ${\ensuremath{\xi}}_{{\ensuremath{\nu}}_{e}}$ and ${\ensuremath{\Omega}}_{b}{h}^{2}$ based upon allowed values consistent with the nucleosynthesis constraints as a function of ${\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\mu},\ensuremath{\tau}}}.$ The change in the background neutrino temperature with degeneracy is also explicitly included, and Gaussian priors for $h=0.72\ifmmode\pm\else\textpm\fi{}0.08$ and the experimental calibration uncertainties are adopted. The marginalized likelihood functions show a slight $(0.5\ensuremath{\sigma})$ preference for neutrino degeneracy. Optimum values with two equally degenerate \ensuremath{\mu} and \ensuremath{\tau} neutrinos imply ${\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\mu},\ensuremath{\tau}}}{=1.0}_{\ensuremath{-}1.0(0.5\ensuremath{\sigma})}^{+0.8(1\ensuremath{\sigma})},$ from which we deduce ${\ensuremath{\xi}}_{{\ensuremath{\nu}}_{e}}{=0.09}_{\ensuremath{-}0.09}^{+0.15},$ and ${\ensuremath{\Omega}}_{b}{h}^{2}{=0.021}_{\ensuremath{-}0.002}^{+0.06}.$ The $2\ensuremath{\sigma}$ upper limit becomes ${\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\mu},\ensuremath{\tau}}}<~2.1,$ which implies ${\ensuremath{\xi}}_{{\ensuremath{\nu}}_{e}}<~0.30,$ and ${\ensuremath{\Omega}}_{b}{h}^{2}<~0.030.$ For only a single large-degeneracy species the optimal value is $|{\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\mu}}}|$ or $|{\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\tau}}}|=1.4$ with a $2\ensuremath{\sigma}$ upper limit of $|{\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\mu}}}|$ or $|{\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\tau}}}|<~2.5.$