  A neutrino Majorana mass generation in the early universe might have left
imprints in cosmological observables. It can source the production of a
detectable stochastic background of primordial gravitational waves with a
spectrum that combines a contribution from a first order phase transition
production and from the vibration of global cosmic strings. An intriguing
possibility is given by the split seesaw model. In this case, in addition to
the traditional high scale seesaw, a low scale neutrino Majorana mass
generation can solve a potential primordial deuterium problem and ameliorate
the cosmological tensions of the $\Lambda$CDM model. At the same time, it can
also produce subdominant contribution to the NANOGrav signal of a stochastic
background of gravitational waves (GWs), in addition to the astrophysical
dominant contribution from supermassive black hole mergers.
