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Do experiments and astrophysical considerations suggest an inverted neutrino mass hierarchy?

The recent results from the Los Alamos neutrino oscillation experiment, together with assumptions of neutrino oscillation solutions for the solar and atmospheric neutrino deficit problems, may place powerful constraints on any putative scheme for neutrino masses and mixings. Assuming the validity of these experiments and assumptions, we argue that a nearly unique spectrum of neutrino masses emerges as a fit, if two additional astrophysical arguments are adopted: (1) the sum of the light neutrino masses is $\sim 5\ {\rm eV}$, as large scale structure simulations with mixed cold plus hot dark matter seem to suggest; and (2) $r$-process nucleosynthesis originates in neutrino-heated ejecta from Type II supernovae. In this fit, the masses of the neutrinos must satisfy $m_{ν_e} \approx m_{ν_s} \approx 2.7\ {\rm eV}$ (where $ν_e$ is split from a sterile species, $ν_s$, by $\sim {10}^{-6} \ {\rm eV}$) and $m_{ν_τ} \approx m_{ν_μ} \approx 1.1\ {\rm eV}$ (where these species are split by $\sim {10}^{-2} \ {\rm eV}$). We discuss alternative neutrino mass spectra that are allowed if we decline to adopt certain experiments or astrophysical models.