# Higgs domain walls in the thermal background

## TL;DR

This paper studies how a thermal background affects Higgs domain walls in the early universe, showing they are unstable, decay quickly, and have negligible impact on cosmological observations.

## Contribution

It extends previous work by incorporating temperature effects into the analysis of Higgs domain walls, revealing their instability and minimal cosmological influence.

## Key findings

- Higgs domain walls are highly unstable in a thermal background.
- The local maximum and domain wall width depend strongly on temperature.
- Domain walls decay shortly after formation, with negligible cosmological effects.

## Abstract

Most cosmological models predict that the universe was hot and dense at the early stages of it's evolution. In this paper we analyse the influence of the thermal bath of Standard Model particles on the dynamics of cosmological Higgs domain walls. This manuscript poses an~extension of our earlier work in which we investigated the evolution of networks of Higgs domain walls neglecting the impact of temperature variation. Using the thermally corrected effective potential of Standard Model we have found that both the position of the local maximum $h_{max}$ separating minima and the width of domain walls strongly depend on temperature $T$. For temperatures higher than $10^{10}\; \textrm{GeV}$ they respectively increase proportionally and decrease inverse proportionally to the increasing temperature. Thus, the energy scale of the problem follows the value of temperature. Our numerical lattice simulations based on the PRS algorithm reveal that Higgs domain walls in the presence of the background thermal bath are highly unstable and decay shortly after formation. Moreover we have found that the fraction of horizons produced by inflation in which Higgs field expectation value is higher then $h_{max}$ needs to be very low in order for the evolution of the~network of the domain walls to end in the electroweak vacuum. This means that Higgs domain walls necessarily were very rare objects and their average energy density was very small. As a result, the domain walls can not significantly effect cosmological observables.