Spontaneously Broken Lepton Number and Cosmological Constraints on the Neutrino Mass Spectrum

Abstract

The cosmological constraints on neutrino masses can be altered if lepton number is broken globally giving rise to a very weakly coupled Goldstone boson-the Majoron. Then heavy neutrinos can decay sufficiently rapidly by Majoron emission, thereby giving negligible contributions to the mass density of the universe. Specifically, if $M$ is the mass scale associated with lepton number breakdown, for $M\ensuremath{\lesssim}{10}^{6}$ GeV there are no constraints on neutrino masses while for $M$ high enough ($M\ensuremath{\gtrsim}{10}^{9}\ensuremath{-}{10}^{10}$ GeV) the standard bounds remain.