NANOGrav meets Hot New Early Dark Energy and the origin of neutrino mass

It has recently been speculated that the NANOGrav observations point towards a first-order phase transition in the dark sector at the GeV scale [1]. Here, we show that such a phase transition might already have been predicted in the Hot New Early Dark Energy model (Hot NEDE) [2],[3]. There, it was argued that two dark sector phase transitions are the signature of neutrino mass generation through the inverse seesaw mechanism. In particular, an IR phase transition serves a double purpose by resolving the Hubble tension through an energy injection and generating the Majorana mass entry in the inverse seesaw mixing matrix. This usual NEDE phase transition is then accompanied by a UV counterpart, which generates the heavy Dirac mass entry in the inverse seesaw mass matrix of a right-handed neutrino. Here, we investigate if the UV phase transition of the Hot NEDE model can occur at the GeV scale in view of the recent NANOGrav observations.