The split majoron model confronts the NANOGrav signal and cosmological tensions

Abstract: In the light of the evidence of a gravitational wave background from the NANOGrav 15yr data set, we reconsider the split majoron model as a new physics extension of the standard model able to generate a needed contribution to solve the current tension between the data and the standard interpretation in terms of inspiraling supermassive black hole massive binaries. In the split majoron model the seesaw right-handed neutrinos acquire Majorana masses from spontaneous symmetry breaking of global $U(1)_{B-L}$ in a strong first order phase transition of a complex scalar field occurring above the electroweak scale. The final vacuum expectation value couples to a second complex scalar field undergoing a low scale phase transition occurring after neutrino decoupling. Such a coupling enhances the strength of this second low scale first order phase transition and can generate a sizeable primordial gravitational wave background contributing to the NANOGrav 15yr signal. Some amount of extra-radiation is generated after neutron-to-proton ration freeze-out but prior to nucleosynthesis. This can be either made compatible with current upper bound from primordial deuterium measurements or even be used to solve a potential deuterium problem. Moreover, the free streaming length of light neutrinos can be suppressed by their interactions with the resulting majoron background and this mildly ameliorates existing cosmological tensions. Thus cosmological observations nicely provide independent motivations for the model.