  There is a puzzling contradiction: direct observations favor a
low-mass-density universe ($0.2\le\Omega_m\le0.6$), but the only model which
fits universe structure over more than three orders of magnitude in distance
scale has a mix of hot (neutrino) and cold dark matter providing a critical
density universe. Models of an open universe (low $\Omega_m$) or one adding a
cosmological constant ($\Lambda$) to provide a critical energy density
($\Omega_m+ \Omega_\Lambda=1$) have probabilities of $<10^{-3}$. Two-neutrino
dark matter works better than having the needed $\sim5$ eV of neutrino mass in
one species of neutrino, and this is consistent with the only model which fits
all present indications for neutrino mass: $\nu_\mu\to\nu_\tau$ accounting for
the atmospheric anomaly (with $\nu_\mu$ and $\nu_\tau$ being the hot dark
matter), $\bar\nu_\mu\to\bar\nu_e$ being observed by LSND, and $\nu_e\to\nu_s$
explaining the solar $\nu_e$ deficit. The LSND/KARMEN results are consistent
with the needed mass of hot dark matter. Further support for this mass pattern
is provided by the need for the sterile neutrino, $\nu_s$, to make possible
heavy-element nucleosynthesis in supernovae. It is a fascinating question as to
whether the hot dark matter paradox will be resolved by better measurements or
by the introduction of new physics.
