Neutrinos of non-zero rest mass and the equivalence principle

TL;DR

This paper explores the implications of neutrinos having non-zero rest mass on cosmological mass density and tests the equivalence principle by considering different gravitational and inertial masses, deriving bounds on their mass and mass ratio.

Contribution

It introduces bounds on neutrino mass from cosmological considerations and examines the possibility of violation of the equivalence principle through differing gravitational and inertial masses.

Findings

Neutrino mass is constrained between 5 eV/c^2 and 20 eV/c^2 based on cosmological density.

The ratio of gravitational to inertial mass (r) is bounded between 0.03 and 6.3.

Neutrinos could violate the equivalence principle within the derived bounds.

Abstract

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.