Gravitational echoes of lepton number symmetry breaking with light and ultralight Majorons

We formulate a version of the low-scale Majoron model equipped with an inverse seesaw mechanism featuring lepton-number preserving dimension-6 operators in the scalar potential. Contrary to its dimension-4 counterpart, we find that the model can simultaneously provide light and ultralight Majorons, neutrino masses and their mixing, while featuring strong first-order cosmological phase transitions associated to the spontaneous breaking of the lepton number and the electroweak symmetries in the early Universe. We show by a detailed numerical analysis under which circumstances the model can be probed via the primordial gravitational wave spectrum potentially observable at LISA and other planned facilities. We discuss which implications result for collider physics observables, such as scalar trilinear couplings, the scalar mixing angle and the mass of a new CP-even Higgs boson.