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 $(\omegab h^2,\xinumt, \xinue, Ω_Λ,h,n)$ plus the calibaration uncertainties. We consider flat ${\Omega }_M+{\Omega }_{\Lambda }=1$ cosmological models with two identical degenerate neutrino species, $\xinumt \equiv \vert \xinum \vert = \vert \xinut \vert$ and a small $\xinue$. We assign weak top-hat priors on the electron-neutrino degeneracy parameter $\xinue$ and ${\Omega }_b{h}^2$ based upon allowed values consistent with the nucleosynthesis constraints as a function of $\xinumt$. 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 $\xinumt = 1.0^{+0.8 (1σ)}_{-1.0 (0.5σ)}$, from which we deduce ${\xi }_{{\nu }_e}=0.09_{-0.09}^{+0.15}$, and ${\Omega }_b{h}^2=0.021_{-0.002}^{+0.06}$. The $2\sigma$ upper limit becomes $ \xinumt \le 2.1$, which implies ${\xi }_{{\nu }_e}\le 0.30$, and ${\Omega }_b{h}^2\le 0.030$. For only a single large-degeneracy species the optimal value is $\vert \xinum \vert$ or $\vert \xinut \vert = 1.4$ with a $2\sigma$ upper limit of $\vert \xinum \vert$ or $\vert \xinut \vert \le 2.5$

8 pages, 5 figures, Phys. Rev. D. Submitted

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