Neutrino Degeneracy and Decoupling: New Limits from Primordial Nucleosynthesis and the Cosmic Microwave Background

We reanalyze the cosmological constraints on the existence of a net universal lepton asymmetry and neutrino degeneracy. We show that neutrinos can begin to decouple at higher temperatures than previous estimates due to several corrections which diminish the neutrino reaction rate. These decoupled neutrinos are therefore not heated as the particle degrees of freedom change. The resultant ratio of the relic neutrino-to-photon temperatures after $e^\pm$ annihilation can then be significantly reduced by more than a factor of two from that of the standard nondegenerate ratio. This changes the expansion rate and subsequent primordial nucleosynthesis, photon decoupling, and structure formation. In particular we analyze physically plausible lepton-asymmetric models with large $\nu_\mu$ and $\nu_\tau$ degeneracies together with a moderate $\nu_e$ degeneracy. We show that the nucleosynthesis by itself permits very large neutrino degeneracies $0 \le \xinum$, $\xinut \le 40$, $0 \le \xinue \le 1.4$ together with large baryon densities $0.1 \le \Omega_b \h502 \le 1$ as long as some destruction of primordial lithium has occurred. We also show that structure formation and the power spectrum of the cosmic microwave background allows for the possibility of an $\Omega = 1$, $\Omega_\Lambda = 0.4$, cosmological model for which there is both significant lepton asymmetry ($| \xinum | = | \xinut | \approx 11$) and a relatively large baryon density ($\Omega_b \h502 \approx 0.2$). Our best-fit neutrino-degenerate, high-baryon-content models are mainly distinguished by a suppression of the second peak in the microwave background power spectrum. This is consistent with the recent high resolution data from BOOMERANG and MAXIMA-1.