Majorana neutrinos, nucleosynthesis, and the lepton asymmetry of the Universe

Abstract

The lepton asymmetry $L\ensuremath{\simeq}\frac{({n}_{\ensuremath{\nu}}\ensuremath{-}{n}_{\overline{\ensuremath{\nu}}})}{{n}_{\ensuremath{\gamma}}}$ of the Universe is one of the main uncertainties in the standard hot big-bang cosmological model. Direct limits on $L$ from the total energy density of the Universe are extremely weak ($|L|<4\ifmmode\times\else\texttimes\fi{}{10}^{4}$), and Harvey and Kolb have recently shown that it is possible to construct grand unified theories in which $L$ is much larger than the baryon asymmetry $B\ensuremath{\sim}{10}^{\ensuremath{-}10}$. On the other hand, many authors have pointed out that the standard scenario for nucleosynthesis would be significantly altered if $|L|$ were of order unity. In this paper we consider the role of the lepton-number violation associated with Majorana neutrino masses in the 10-eV range in reducing an initial large lepton asymmetry. We find that in most models with explicit hard lepton-number violation any initial lepton asymmetry would be reduced to an insignificant level long before nucleosynthesis. For models in which lepton number is violated spontaneously (or relies on S${\mathrm{U}}_{2}$\ifmmode\times\else\texttimes\fi{}${\mathrm{U}}_{1}$ breaking), we utilize an argument due to Linde that a large initial lepton asymmetry would prevent the restoration of S${\mathrm{U}}_{2}$\ifmmode\times\else\texttimes\fi{}${\mathrm{U}}_{1}$ (and of lepton number) in the early Universe. For a large class of models and initial conditions, the asymmetry of the lightest neutrino species would be reduced to a fixed-point value of order unity, prior to nucleosynthesis, while the asymmetries in the more massive neutrinos would be driven to negligible levels. This is precisely the range for which the neutrino asymmetries would significantly affect nucleosynthesis.