The discovery of gravitational waves open new opportunities to test new physics.
In particular, the production of a stochastic background of primordial gravitational waves could
be associated to the generation of the right-right Majorana neutrino mass term.
This is necessary within the seesaw mechanism to explain the lightness of neutrinos and their mixing parameters measured in neutrino oscillation parameters. I will discuss the possibility that such a generation is described within Majoron models and occurs during a strong first order phase transition [1]. As well known, this can indeed produce a stochasticbackground of gravitational waves. The scale of the phase transition can or cannot coincide with the seesaw scale.In the latter case a low scale phase transition, occurring in the pre-recombination era, might be tested at very low frequencies ($10^{-9}$--$10^{-6}\,{\rm Hz}$). Even though the signal can hardly reproduce the NANOGrac putative signal such new physics at low scale might help ameliorating the tensions in the $\L$CDM cosmological model (e.g., the Hubble tension). I will also discuss how a phase transition might be responsible for the generation of dark matter in the form of dark neutrinos coupling to the seesaw neutrinos via Higgs induced right handed-right handed neutrino mixing [2].