Probing the high temperature symmetry breaking with gravitational waves from domain walls

TL;DR

This paper investigates how gravitational waves from domain wall annihilation can probe high temperature symmetry breaking, especially the $ ext{Z}_2$ symmetry, with potential observability by future GW detectors and implications for NANOGrav signals.

Contribution

It introduces a model with a scalar and singlet fermions to study high temperature $ ext{Z}_2$ symmetry breaking and predicts observable gravitational wave signals from domain wall annihilation.

Findings

GW signals from domain walls at $ ext{O}(10^{9})$ GeV are detectable by BBO, CE, and ET.

The scenario can potentially explain or relate to NANOGrav signals.

The model demonstrates the connection between high temperature symmetry breaking and gravitational wave phenomenology.

Abstract

The symmetry can be broken at high temperature and then restored at low temperature, which is the so-called \emph{high temperature symmetry breaking}. It often appears in some theories such as the high scale electroweak baryogenesis mechanism. In this paper, we probe the high temperature $\mathbb{Z}_2$ symmetry breaking with gravitational waves (GWs) from domain wall annihilation. We first introduce a scalar with $\mathbb{Z}_2$ symmetry and few of singlet fermions that interact with scalar through a five-dimension operator. This can lead to the scalar potential has a non-zero minimum at high temperature. At the early stage, the scalar is pinned at symmetric phase due to the large Hubble fraction. When the scalar thermal mass becomes comparable to the Hubble parameter, it can quickly roll down to the minimum of potential. Then the $\mathbb{Z}_2$ symmetry is spontaneously broken and the domain walls will form. With the decrease of temperature, $\mathbb{Z}_2$ symmetry will be restored. We find that if domain walls are formed at $\mathcal{O}(10^{9})~ \rm GeV$, the GW produced by domain wall annihilation is expected to be observed by BBO, CE and ET. In addition, we also discuss the relationships between this scenario and NANOGrav signal.