Evolution of FLRW spacetime after the birth of a cosmic string

TL;DR

This paper investigates how an FLRW universe evolves after a cosmic string forms, analyzing perturbations, metric properties, and causality to extend previous models of string-induced spacetime changes.

Contribution

It generalizes prior work on Nambu-Goto strings by analyzing scalar and tensor perturbations and their effects on spacetime and causality after cosmic string formation.

Findings

Deficit angle and shock front within the light cone and horizon

Perturbations maintain energy conservation and causality

Explicit coordinate transformations demonstrate no causality violation

Abstract

We consider the evolution of an initially FLRW universe after the formation of a long, straight, cosmic string with arbitrary tension and mass per unit length. The birth of the string sources scalar and tensor-type perturbations in the background metric and both density and velocity perturbations in the background fluid, which compensate for the string mass and maintain energy conservation. The former generate the deficit angle within the light cone of the string and a gravitational shock front at the cosmological horizon, whereas the latter are confined within the sound cone. We study the properties of the metric within each region of the resulting spacetime and give the explicit coordinate transformations which demonstrate non-violation of causality. This paper generalizes the work of previous studies for the Nambu-Goto string.