Domain wall annihilation -- a QFT perspective

TL;DR

This paper develops a quantum field theoretical approach to analyze the formation, evolution, and annihilation of domain wall networks in the early universe, providing a new analytic law for their area density decay.

Contribution

It introduces a novel quantum field theory method to study domain wall dynamics, including initial state treatment and evolution, with a derived decay law for wall area density.

Findings

Derived a decay law: $t^{-1/2}\, ext{exp}(- (t/t_{ann})^{d/2})$ for domain wall area density.

Connected the new analytic results with previous condensed matter and cosmological studies.

Discussed applicability to expanding universe scenarios near the domain wall 'gas' limit.

Abstract

Domain wall networks in the early universe, formed upon spontaneous breaking of a discrete symmetry, have a rich impact on cosmology. Yet, they remain somewhat unexplored. We introduce a new analytic strategy to understand better the domain wall epoch, from formation to annihilation. Our method includes a quantum field theoretical treatment of the initial state at domain wall formation, as well as of the time evolution. We find that the domain wall area density for a network with biased initial condition in $d+1$ dimensional flat spacetime evolves as $t^{-1/2}\,\exp\big(- (t/t_{ann})^{d/2}\big)$. We comment on the relation between this and previous results obtained in condensed matter and in cosmology. The extrapolation of this law to an expanding universe applies to networks that are close to the domain wall `gas' limit.