Cold Plus Hot Dark Matter Cosmology in the Light of Solar and Atmospheric Neutrino Oscillations

We explore the implications of possible neutrino oscillations, as indicated by the solar and atmospheric neutrino experiments, for the cold plus hot dark matter scenario of large scale structure formation. We find that there are essentially three distinct schemes that can accommodate the oscillation data and which also allow for dark matter neutrinos. These include (i) three nearly degenerate (in mass) neutrinos, (ii) non-degenerate masses with $\nu_\tau$ in the eV range, and (iii) nearly degenerate $\nu_\mu-\nu_\tau$ pair (in the eV range), with the additional possibility that the electron neutrino is cosmologically significant. The last two schemes invoke a `sterile' neutrino which is light (< or ~ eV). We discuss the implications of these schemes for $\bar{\nu}_\mu - \bar{\nu}_e$ and $\nu_\mu - \nu_\tau$ oscillation, and find that scheme (ii) in particular, predicts them to be in the observable range. As far as structure formation is concerned, we compare the one neutrino flavor case with a variety of other possibilities, including two and three degenerate neutrino flavors. We show, both analytically and numerically, the effects of these neutrino mass scenarios on the amplitude of cosmological density fluctuations. With a Hubble constant of 50 km s$^{-1}$ Mpc$^{-1}$, a spectral index of unity, and $\Omega_{baryon} = 0.05$, the two and three flavor scenarios fit the observational data marginally better than the single flavor scheme. However, taking account of the uncertainties in these parameters, we show that it is premature to pick a clear winner.Comment: 1 LaTEX file plus 1 uuencoded Z-compressed tar file with 3 postscript figure