Simulating the symmetron: domain walls and symmetry-restoring impurities

TL;DR

This paper investigates how relativistic domain walls interact with static impurities in the symmetron model, revealing pinning effects, energetically favored configurations, and altered network scaling laws.

Contribution

It introduces a detailed numerical study of domain wall dynamics with symmetry-restoring impurities in the symmetron framework, highlighting new behaviors and scaling modifications.

Findings

Domain walls pin to impurities.

Domain wall necklaces can be energetically favored.

Impurities modify the standard domain wall network scaling law.

Abstract

In this paper we study the dynamics of relativistic domain walls in the presence of static symmetry-restoring impurities. The field theory is precisely the same as what is known to cosmologists as the "symmetron model", whereby the usual $\mathbb{Z}_2$ symmetry breaking potential is appended with a space-varying mass-term (the space-variation is set by the profile of the impurity, which we take to be a "tanh"-function). After presenting the outcomes of a suite of different numerical experiments we have three main results: (1) domain walls pin to impurities, (2) domain wall necklaces can be energetically preferred configurations, and (3) impurities significantly modifies the usual ${N}_{\rm dw}\propto t^{-1}$ scaling law for random networks of domain walls.