Lepton asymmetry and primordial nucleosynthesis in the era of precision cosmology

Abstract

We calculate and display the primordial light-element abundances as a function of a neutrino degeneracy parameter $\ensuremath{\xi}$ common to all flavors. It is the only unknown parameter characterizing the thermal medium at the primordial nucleosynthesis epoch. The observed primordial helium abundance ${Y}_{\mathrm{p}}$ is the most sensitive cosmic ``leptometer.'' Adopting the conservative ${Y}_{\mathrm{p}}$ error analysis of Olive and Skillman implies $\ensuremath{-}0.04\ensuremath{\lesssim}\ensuremath{\xi}\ensuremath{\lesssim}0.07$ whereas the errors stated by Izotov and Thuan imply $\ensuremath{\xi}=0.0245\ifmmode\pm\else\textpm\fi{}0.0092$ ($1\ensuremath{\sigma}$). Improved determinations of the baryon abundance have no significant impact on this situation. A determination of ${Y}_{\mathrm{p}}$ that reliably distinguishes between a vanishing or nonvanishing $\ensuremath{\xi}$ is a crucial test of the cosmological standard assumption that sphaleron effects equilibrate the cosmic lepton and baryon asymmetries.