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Recent Kamiokande data supports the $\nu_\mu \to \nu_\tau$ neutrino oscillation explanation of the deficit of cosmic ray muon neutrinos, which requires that the muon and tau neutrinos have almost identical masses. Preliminary evidence from the current Los Alamos neutrino oscillation experiment suggests that the mass of the muon neutrino $m(\nu_\mu)$ is $\sim 2.4$ eV. Two neutrinos of mass 2.4 eV each would constitute ``hot" dark matter accounting for a fraction $\Omega_\nu = 0.05 h^{-2}$ of critical density, where $h \equiv H_0/(100 {\rm km/s/Mpc})$ is the Hubble parameter.
We consider the consequences of such neutrino masses for cosmological models for the formation of galaxies and large scale structure in the universe, which are spatially flat and in which most of the dark matter is ``cold." Linear calculations and N-body simulations indicate that an $\Omega=1$ Cold + Hot Dark Matter (CHDM) cosmological model with two neutrinos each of mass $\approx 2.4$ eV agrees remarkably well with all available observations. However, we find that this is true only if the Hubble parameter $h \approx 0.5$. We also consider Cold Dark Matter (CDM) models with a cosmological constant $\Lambda$ and show that evidence for hot dark matter raises serious difficulties for low-$\Omega$ $\Lambda$CDM models.
