Can a mass inversion save solar neutrino oscillations from the LSND neutrino?

In the light of the νμ → νe neutrino oscillations which may have been observed at the LSND experiment we explore the consequences of two inverted mass schemes where solar neutrino oscillations occur between νe and ντ. One favored LSND value, Δm2 = 6 eV2, leads to mνe ≈ mντ ≈ 2.5 eV and mνμ ≈ 0 so that cosmology can benefit from a recently proposed “cold plus hot dark matter” structure formation scenario with scenario with two equal mass light neutrinos (Cν2DM). Solar neutrino oscillations (νe → ντ) can occur with one of the large mixing angle solutions so that a serious conflict with ββ decay Majorana mass limits is avoided without invoking Dirac masses. However, there is a problem with the SN 1987A signal because of resonant νe ↔ νμ oscillations which are expected to cause far higher νe energies at the IMB and Kamiokande II detectors than have been observed. A small value Δm2 ≈ 0.5 eV2 at LSND, which allows for a relatively large νe−νμ mixing angle without conflicting with the KARMEN and BNL-E776 experiments, would indicate mνe ≈ mντ ≈ 1.6eV and mνμ ≈ 1.8eV. This scheme of Cν3DM maintains, and even may improve, the essential cosmological model implications for large-scale structure, leaving no conflict with SN r-process nucleosynthesis.