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4. Hot Dark Matter Density Omeganu

The recent atmospheric neutrino data from Super-Kamiokande (Fukuda et al. 1998) provide strong evidence of neutrino oscillations and therefore of non-zero neutrino mass. These data imply a lower limit on the hot dark matter (i.e., light neutrino) contribution to the cosmological density Omeganu gtapprox 0.001. Omeganu is actually that low, and therefore cosmologically uninteresting, if m(nutau) >> m(nuµ), as is suggested by the hierarchical pattern of the quark and charged lepton masses. But if the nutau and nuµ are nearly degenerate in mass, as suggested by their strong mixing, then Omeganu could be substantially larger. Although the Cold + Hot Dark Matter (CHDM) cosmological model with h approx 0.5, Omegam = 1, and Omeganu = 0.2 predicts power spectra of cosmic density and CMB anisotropies that are in excellent agreement with the data (Primack 1997, Gawiser & Silk 1998), as we have just seen the large value measured for the Hubble parameter makes such Omegam = 1 models dubious. It remains to be seen whether including a significant amount of hot dark matter in low-Omegam models improves their agreement with data. Primack & Gross (1998) found that the possible improvement of the low-Omegam flat (LambdaCDM) cosmological models with the addition of light neutrinos appears to be rather limited, and the maximum amount of hot dark matter decreases with decreasing Omegam (Primack et al. 1995). For Omegam ltapprox 0.4, Croft, Hu, and Davé (1999) find that Omeganu ltapprox 0.08. Fukugita et al. (1999) find more restrictive upper limits with the constraint that the primordial power spectrum index n leq 1, but this may not be well motivated.