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 $Ω_M + Ω_Λ= 1$ 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 $Ω_b h^2$ 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$σ$) preference for neutrino degeneracy. Optimum values with two equally degenerate $μ$ and $τ$ neutrinos imply $\xinumt = 1.0^{+0.8 (1σ)}_{-1.0 (0.5σ)}$, from which we deduce $ξ_{ν_e} = 0.09^{+0.15}_{-0.09}$, and $Ω_b h^2 = 0.021^{+0.06}_{- 0.002}$. The $2σ$ upper limit becomes $ \xinumt \le 2.1$, which implies $ξ_{ν_e} \le 0.30$, and $Ω_b h^2 \le 0.030$. For only a single large-degeneracy species the optimal value is $\vert \xinum \vert$ or $\vert \xinut \vert = 1.4$ with a $2σ$ upper limit of $\vert \xinum \vert$ or $\vert \xinut \vert \le 2.5$