Constraints on Neutrino Degeneracy from the Cosmic Microwave Background and Primordial Nucleosynthesis

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 $(\omegab h^2,\xinumt, \xinue, \Omega_\Lambda,h,n)$plusthecalibarationuncertainties\mathrm{.}Weconsiderflat$\Omega_M + \Omega_\Lambda = 1$ cosmological models with two identical degenerate neutrino species, $\xinumt \equiv \vert \xinum \vert = \vert \xinut \vert$andasmall$\xinue$. We assign weak top-hat priors on the electron-neutrino degeneracy parameter $\text{xinue}$ and ${\mathrm{\Omega }}_b{h}^2$ based upon allowed values consistent with the nucleosynthesis constraints as a function of $\text{xinumt}$. The change in the background neutrino temperature with degeneracy is also explicitly included, and Gaussian priors for $h=0.72\pm 0.08$ and the experimental calibration uncertainties are adopted. The marginalized likelihood functions show a slight (0.5$\sigma$) preference for neutrino degeneracy. Optimum values with two equally degenerate $\mu$ and $\tau$ neutrinos imply $\text{xinumt}=1.0_{-1.0(0.5\sigma )}^{+0.8(1\sigma )}$, from which we deduce ${\xi }_{{\nu }_e}=0.09_{-0.09}^{+0.15}$, and $\Omega_b h^2 = 0.021^{+0.06}{- 0.002}$\mathrm{.}The$2\sigma$upperlimitbecomes$ \xinumt \le 2.1$,whichimplies$\xi{\nu_e} \le 0.30$,and$\Omega_b h^2 \le 0.030$. For only a single large-degeneracy species the optimal value is $\mathrm{\mid }\text{xinum}\mathrm{\mid }$ or $\vert \xinut \vert = 1.4$witha$2\sigma$upperlimitof$\vert \xinum \vert$or$\vert \xinut \vert \le 2.5$