Lepton parity dark matter and naturally unstable domain walls

TL;DR

This paper links neutrino masses, dark matter, and gravitational waves through a minimal lepton parity scenario, where unstable domain walls from spontaneous symmetry breaking produce observable gravitational wave signals.

Contribution

It introduces a simple model connecting neutrino masses, dark matter stability, and gravitational wave production via domain wall dynamics without extra symmetries.

Findings

Dark matter is stabilized by residual lepton parity symmetry.

Spontaneous breaking of an accidental  symmetry leads to unstable domain walls.

Domain wall annihilation produces a potentially observable gravitational wave background.

Abstract

We propose a simple and predictive setup that connects neutrino masses, dark matter (DM), and gravitational waves. A minimal lepton parity DM scenario is considered where the residual symmetry $(-1)^L$ from the type I seesaw acts as the dark parity $D=(-1)^{L+2j}$, ensuring DM stability without imposing any new symmetry. A singlet Majorana fermion $S$ with even lepton parity serves as the DM candidate, interacting via a real scalar $\sigma$ which is also even lepton parity. The scalar potential possesses an accidental $\mathcal{Z}_2$ symmetry, whose spontaneous breaking gives rise to unstable domain walls (DW) in the presence of explicit $\mathcal{Z}_2$ breaking terms allowed by the lepton parity. The subsequent DW annihilation generates a stochastic gravitational wave (GW) background potentially observable at different GW experiments.