Global String Instantons

TL;DR

This paper investigates the quantum tunneling process leading to the formation of gravitating global strings, analyzing instanton solutions and their implications for spacetime structure and quantum cosmology.

Contribution

It provides a comprehensive numerical analysis of instantons for gravitating global strings across various parameters, extending understanding of topological defect nucleation.

Findings

Instantons characterized by core thickness and gravitational backreaction are numerically obtained.

Configurations become homogeneous beyond certain thresholds, similar to Hawking-Moss solutions.

Analytic continuation reveals anisotropic universe regions in spacetime.

Abstract

We study the formation of gravitating global strings through quantum mechanical tunneling. The instantons that describe the nucleation process are characterized by two parameters: the string core thickness and its gravitational backreaction controlled by the string core energy density. We obtain solutions across a wide range of these parameters by carrying out numerical integration via multiple shooting methods. Our results are in agreement with previous findings on the nucleation of other topological defects; specifically, after reaching a certain threshold for the string core thickness or its gravitational backreaction, the configuration becomes homogeneous in a manner akin to Hawking-Moss solutions. Additionally, we analyze the global structure of the analytical continuation of the solutions to Lorentzian signature, revealing the emergence of a region of spacetime that describes an anisotropic universe. Finally, we also discuss the relevance of these instantons in the context of quantum cosmology.