Cosmological measurement of neutrino mass in the presence of leptonic asymmetry

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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.