Initial condition of a thick loop cosmic string and linear perturbations

TL;DR

This paper investigates the initial gravitational data of thick loop cosmic strings, identifying a critical thickness where linear perturbation theory breaks down, and providing conditions under which linear analysis remains valid.

Contribution

It introduces the concept of a critical string thickness and analyzes the validity of linear perturbation theory for thick loop cosmic strings.

Findings

Thick loops are not geodesic on the initial hypersurface.

A conical singularity is geodesic, unlike the thick loop.

Linear perturbation theory is valid if string thickness exceeds ~5×10^{-3} times the loop's curvature radius.

Abstract

The initial data of the gravitational field produced by a loop thick string is considered. We show that a thick loop is not a geodesic on the initial hypersurface, while a loop conical singularity is. This suggests that there is the ``{\it critical thickness}'' of a string, at which the linear perturbation theory with a flat space background fails to describe the gravity of a loop cosmic string. Using the above initial data, we also show that the linear perturbation around flat space is plausible if the string thickness is larger than $\sim5\times10^{-3}a$, where $a$ is the curvature radius of the loop.