Neutrinos of non-zero rest mass and the equivalence principle

Assuming that neutrinos of non-zero rest mass dominate the mass density in the universe, and also the mass density on the scale of clusters of galaxies, one obtains the upper limit m < 20 eV/c^2 on their mass, independent of the values of H_0 and q_0, and the lower limit m > 5 eV/c^2 independent of q_0 and almost independent of H_0. If they are not to dominate the mass density on the scale of binary galaxies and small groups of galaxies, one must have m < 14 eV/c2 independent of q0 and almost independent of H0. Going one step further, we allow neutrinos to have different gravitational and inertial masses so that r = gravitational / inertial mass. Then using m for the inertial mass, we have m.r^1/4 > 5 eV/c^2, m.r^(1/4) < 14 eV/c^2 and m.r < 20 eV/c^2, which together imply r < 6.3. For a specific value, say, 12 eV/c^2, for m, we have 0.03 < r < 1.7. Keywords: Neutrinos, rest mass, equivalence principle.