  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.

High Energy Physics - Phenomenology;Astrophysics