Self-gravitating global monopole and nonsingular cosmology

TL;DR

This paper reviews properties of spherically symmetric global monopoles in higher-dimensional general relativity, revealing various solution types, including regular, horizon-containing, and oscillating Higgs field solutions, with implications for nonsingular cosmology.

Contribution

It identifies and analyzes new classes of solutions for global monopoles in higher dimensions, including regular and oscillating Higgs field configurations, and explores their cosmological implications.

Findings

Existence of six qualitative behavior types of monopole solutions.

Identification of parameter ranges for regular solutions with horizons.

Discovery of oscillating Higgs field solutions with finite space-time regions.

Abstract

We review some recent results concerning the properties of a spherically symmetric global monopole in $(D=d+2)$-dimensional general relativity. Some common features of monopole solutions are found independently of the choice of the symmetry-breaking potential. Thus, the solutions show six types of qualitative behavior and can contain at most one simple horizon. For the standard Mexican hat potential, we analytically find the $D$-dependent range of $\gamma$ (the gravitational field strength parameter) in which there exist globally regular solutions with a monotonically growing Higgs field, containing a horizon and a Kantowski-Sachs (KS) cosmology outside it, where the topology of spatial sections is $\R\times \S^d$. Their cosmological properties favor the idea that the standard Big Bang might be replaced with a nonsingular static core and a horizon appearing as a result of some symmetry-breaking phase transition on the Planck energy scale. We have also found families of new solutions with an oscillating Higgs field, parametrized by the number of its knots. All such solutions describe space-times of finite size, possessing a regular center, a horizon and a singularity beyond it.