  We show how the generation of right-handed neutrino masses in Majoron models
may be associated with a first-order phase transition and accompanied by the
production of a stochastic background of gravitational waves (GWs). We explore
different energy scales with only renormalizable operators in the effective
potential. If the phase transition occurs above the electroweak scale, the
signal can be tested by future interferometers. We consider two possible energy
scales for phase transitions below the electroweak scale. If the phase
transition occurs at a GeV, the signal can be tested at LISA and provide a
complementary cosmological probe to right-handed neutrino searches at the FASER
detector. If the phase transition occurs below 100 keV, we find that the peak
of the GW spectrum is two or more orders of magnitude below the putative
NANOGrav GW signal at low frequencies, but well within reach of the SKA and
THEIA experiments. We show how searches of very low frequency GWs are motivated
by solutions to the Hubble tension in which ordinary neutrinos interact with
the dark sector. We also present general calculations of the phase transition
temperature and Euclidean action that apply beyond Majoron models.
