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

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.