An inverted neutrino mass hierarchy for hot dark matter and the solar neutrino deficit

The cosmological model in which 20% of the dark matter is shared by two nearly equal mass neutrinos fits the structure of the universe on all scales. This has been motivated by a νμ → ντ oscillation explanation of the deficit of atmospheric νμʹs. If the observed atmospheric νμνe ratio has an alternative explanation, the cosmological model can be retained if the deficit of solar neutrinos is explained by νe → ντ oscillation. In this case, an inverted neutrino mass hierarchy is required with mνμ ⪡ mνe ≈ mντ ≈ 2.4 eV. We show that if there exists an Le − Lτ symmetry in nature, then both the near mass degeneracy of νe and ντ, as well as the consistency of the above values for neutrino masses with the negative results of the neutrinoless double beta decay search experiments are easily understood. We show that this symmetry implemented in the context of a high-scale left-right symmetric model with the see-saw mechanism can lead to a simple theoretical understanding of the desired form of the mass matrix.