Evolution of Topological Defects During Inflation

TL;DR

This paper investigates how the expansion of the universe during inflation affects the internal structure of topological defects, finding that only thin defects smaller than a critical size remain stable, while thicker ones are smoothed out.

Contribution

It provides a detailed analysis of the impact of inflationary expansion on topological defects, identifying a critical thickness beyond which defects cannot maintain stationary solutions.

Findings

Thin defects are well approximated by flat space solutions.

Defects thicker than a critical size are smeared out by expansion.

No stationary solutions exist for defects exceeding the critical thickness.

Abstract

Topological defects can be formed during inflation by phase transitions as well as by quantum nucleation. We study the effect of the expansion of the Universe on the internal structure of the defects. We look for stationary solutions to the field equations, i.e. solutions that depend only on the proper distance from the defect core. In the case of very thin defects, whose core dimensions are much smaller than the de Sitter horizon, we find that the solutions are well approximated by the flat space solutions. However, as the flat space thickness parameter $\delta_0$ increases we notice a deviation from this, an effect that becomes dramatic as $\delta_0$ approaches $(H)^{-1}/{\sqrt 2}$. Beyond this critical value we find no stationary solutions to the field equations. We conclude that only defects that have flat space thicknesses less than the critical value survive, while thicker defects are smeared out by the expansion.