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We show how the generation of right-handed neutrino masses in Majoron modelsmay be associated with a first-order phase transition and accompanied by theproduction of a stochastic background of gravitational waves (GWs). We exploredifferent energy scales with only renormalizable operators in the effectivepotential. If the phase transition occurs above the electroweak scale, thesignal can be tested by future interferometers. We consider two possible energyscales for phase transitions below the electroweak scale. If the phasetransition occurs at a GeV, the signal can be tested at LISA and provide acomplementary cosmological probe to right-handed neutrino searches at the FASERdetector. If the phase transition occurs below 100 keV, we find that the peakof the GW spectrum is two or more orders of magnitude below the putativeNANOGrav GW signal at low frequencies, but well within reach of the SKA andTHEIA experiments. We show how searches of very low frequency GWs are motivatedby solutions to the Hubble tension in which ordinary neutrinos interact withthe dark sector. We also present general calculations of the phase transitiontemperature and Euclidean action that apply beyond Majoron models.

Gravitational waves from first-order phase transitions in Majoron models of neutrino mass