Gravitational Waves in an A4 Neutrino Mass Model

The A4 flavor symmetry has provided tremendous insight into the flavor structure of the lepton sector of the Standard Model, predicting a very good approximation to neutrino mixing angles, Tri-Bimaximal Mixing. A4 is spontaneously broken by a scalar called the flavon, and when this happens a number of degenerate vacua can form, resulting in so-called domain walls. These objects are not observed and hence need to be annihilated. This is usually done by explicitly breaking A4 by adding a bias term to the scalar potential. In this paper, we construct a new model invariant under A4 and Z4, which creates cosmologically viable domain walls, lifts the degeneracy of the vacuum giving a natural mechanism for domain walls to annihilate, as well as predicts realistic neutrino mixing angles; all utilizing cross couplings between flavons. The annihilation of the domain walls, with proper choice of wall tension and the consequent bias term, leads to a gravitational wave signal that is potentially detectable in near future gravitational wave experiments, and interestingly intersects with the observed Pulsar Timing Array signal.