  We propose a framework to account for neutrino masses at the two-loop level.
This mechanism introduces new scalars and Majorana fermions to the Standard
Model. It is assumed the existence of a global $\mathrm{U(1)\times
\mathcal{Z}_2}$ symmetry which after partial breaking provides the stability of
the dark matter candidates of the theory. The rich structure of the potential
allows for the possibility of first-order phase transitions (FOPTs) in the
early Universe which can lead to the generation of primordial gravitational
waves as one of the potentially observable signatures of this model. Taking
into account relevant constraints from lepton flavour violation, neutrino
physics as well as the trilinear Higgs couplings at next-to-leading order
accuracy, we have found a wide range of possible FOPTs which are strong enough
to be probed at the proposed gravitational-wave interferometer experiments such
as LISA.
