Cosmological measurement of neutrino mass in the presence of leptonic asymmetry

We show that even the smallest neutrino mass consistent with the Super–Kamiokande data is relevant for cosmological models of structure formation and cosmic microwave background (CMB) anisotropies, provided that a relic neutrino asymmetry exists. We calculate the precision with which a 0.07 eV neutrino mass could be extracted from CMB anisotropy and large-scale structure data by the future Planck satellite and Sloan Digital Sky Survey. We find that such a mass can be detected, assuming a large relic neutrino asymmetry still allowed by current experimental data. This measurement of the absolute value of the neutrino mass would be crucial for our understanding of neutrino models.