Dynamics of $Z_N$ domain walls with bias directions

TL;DR

This paper investigates how bias directions influence the dynamics and annihilation times of $Z_N$ domain walls in the early Universe, using numerical simulations to reveal key differences caused by bias orientation.

Contribution

It introduces a detailed numerical study of $Z_N$ domain wall dynamics with bias directions, highlighting the dependence of annihilation time on both vacuum energy difference and bias orientation.

Findings

Domain wall dynamics vary significantly with bias directions.

Annihilation time depends on vacuum energy difference and bias orientation.

Bias directions affect the lifetime and evolution of domain walls.

Abstract

The spontaneous breaking of a discrete symmetry can lead to the formation of domain walls in the early Universe. In this work, we explore the impact of bias directions on the dynamics of $Z_N$ domain walls, mainly focusing on the $N = 3$ model with a biased potential. Utilizing the Press-Ryden-Spergel method, we numerically investigate the dynamics of domain walls with lattice simulations. We find notable differences in the dynamics of domain walls due to bias directions. Our results indicate that the annihilation time depends not only on the vacuum energy difference $\delta V$ but also on bias directions described by the relative potential difference $ \zeta $.