Gravitational waves from supercooled phase transitions in conformal Majoron models of neutrino mass

We study supercooled first-order phase transitions above the QCD scale in a wide class of conformal Majoron-like U(1)' models that explain the totality of active neutrino oscillation data and produce a detectable stochastic gravitational wave background (SGWB) at LIGO, LISA and ET. We place constraints on the U(1)' breaking scale and gauge coupling using current LIGO-Virgo-Kagra data. We find that strong supercooling can be ruled out in large regions of parameter space if a SGWB is not detected by these experiments. A null signal at LIGO and ET will disfavor a type-I seesaw scale above $10^{14}$ GeV, while a positive signal is a signature of heavy right-handed neutrinos. On the other hand, LISA will be sensitive to seesaw scales as low as a TeV, and could detect a SGWB even if the right-handed neutrinos are decoupled.
Comment: 50 pages, 25 figures, 3 tables