Revisiting evolution of domain walls and their gravitational radiation with CosmoLattice

TL;DR

This paper uses numerical simulations with CosmoLattice to study the evolution of domain walls and their gravitational wave signatures in a radiation-dominated universe, revealing key spectral features and the impact of initial conditions.

Contribution

It introduces a new technique to extract gravitational wave spectra from domain wall simulations and provides detailed analysis of domain wall evolution before and after scaling.

Findings

GW spectrum peaks at the Hubble scale

Exponential falloff at scales shorter than wall width

Initial conditions affect GW intensity

Abstract

Employing the publicly available CosmoLattice code, we conduct numerical simulations of a domain wall network and the resulting gravitational waves (GWs) in a radiation-dominated Universe in the $Z_2$-symmetric scalar field model. In particular, the domain wall evolution is investigated in detail both before and after reaching the scaling regime, using the combination of numerical and theoretical methods. We demonstrate that the total area of closed walls is negligible compared to that of a single long wall stretching throughout the simulation box. Therefore, the closed walls are unlikely to have a significant impact on the overall network evolution. This is in contrast with the case of cosmic strings, where formation of loops is crucial for maintaining the system in the scaling regime. To obtain the GW spectrum, we develop a technique that separates physical effects from numerical artefacts arising due to finite box size and non-zero lattice spacing. Our results on the GW spectrum agree well with Refs. [29, 30], which use different codes. Notably, we observe a peak at the Hubble scale, an exponential falloff at scales shorter than the wall width, and a plateau/bump at intermediate scales. We also study sensitivity of obtained results on the choice of initial conditions. We find that different types of initial conditions lead to qualitatively similar domain wall evolution in the scaling regime, but with important variations translating into different intensities of GWs.