Effects of biases in domain wall network evolution. II. Quantitative analysis

TL;DR

This paper provides a detailed quantitative analysis of biased domain wall networks in the early universe, examining their evolution, decay laws, and the validity of analytic models through extensive numerical simulations.

Contribution

It extends previous work by analyzing field distributions, validating the Gaussian approximation, and testing the velocity-dependent one-scale model for anisotropic walls.

Findings

Gaussian approximation validity distinguishes biased potential and initial conditions.

Anisotropic walls reach linear scaling after isotropization.

The velocity-dependent one-scale model accurately predicts the evolution.

Abstract

Domain walls form at phase transitions which break discrete symmetries. In a cosmological context they often overclose the universe (contrary to observational evidence), although one may prevent this by introducing biases or forcing anisotropic evolution of the walls. In a previous work [Correia {\it et al.}, Phys.Rev.D90, 023521 (2014)] we numerically studied the evolution of various types of biased domain wall networks in the early universe, confirming that anisotropic networks ultimately reach scaling while those with a biased potential or biased initial conditions decay. We also found that the analytic decay law obtained by Hindmarsh was in good agreement with simulations of biased potentials, but not of biased initial conditions, and suggested that the difference was related to the Gaussian approximation underlying the analytic law. Here we extend our previous work in several ways. For the cases of biased potential and biased initial conditions we study in detail the field distributions in the simulations, confirming that the validity (or not) of the Gaussian approximation is the key difference between the two cases. For anisotropic walls we carry out a more extensive set of numerical simulations and compare them to the canonical velocity-dependent one-scale model for domain walls, finding that the model accurately predicts the linear scaling regime after isotropization. Overall, our analysis provides a quantitative description of the cosmological evolution of these networks.