Modelling the dynamics of global monopoles

TL;DR

This paper models global monopoles with gravity using a thin wall approximation, revealing conditions for static, inflating, and singular solutions, and supporting the idea that topological defects can undergo inflation.

Contribution

It introduces a detailed analysis of global monopole solutions with gravity, identifying parameter regimes for static, inflating, and metastable configurations, and explores their stability and configuration space.

Findings

Existence of unique static solutions for ta < M_p with negative mass.

Inflating monopole solutions exist for ta ge M_p with cosmological exterior.

Solutions are singular when the gravitational mass M is positive.

Abstract

A thin wall approximation is exploited to describe a global monopole coupled to gravity. The core is modelled by de Sitter space; its boundary by a thin wall with a constant energy density; its exterior by the asymptotic Schwarzschild solution with negative gravitational mass $M$ and solid angle deficit, $\Delta\Omega/4\pi = 8\pi G\eta^2$, where $\eta$ is the symmetry breaking scale. The deficit angle equals $4\pi$ when $\eta=1/\sqrt{8\pi G} \equiv M_p$. We find that: (1) if $\eta <M_p$, there exists a unique globally static non-singular solution with a well defined mass, $M_0<0$. $M_0$ provides a lower bound on $M$. If $M_0<M<0$, the solution oscillates. There are no inflating solutions in this symmetry breaking regime. (2) if $\eta \ge M_p$, non-singular solutions with an inflating core and an asymptotically cosmological exterior will exist for all $M<0$. (3) if $\eta$ is not too large, there exists a finite range of values of $M$ where a non-inflating monopole will also exist. These solutions appear to be metastable towards inflation. If $M$ is positive all solutions are singular. We provide a detailed description of the configuration space of the model for each point in the space of parameters, $(\eta, M)$ and trace the wall trajectories on both the interior and the exterior spacetimes. Our results support the proposal that topological defects can undergo inflation.