The Universe as a Topological Defect in a Higher-Dimensional Einstein-Yang-Mills Theory

TL;DR

This paper proposes that our universe can be viewed as a topological defect, specifically a vortex, arising from spontaneous compactification in a higher-dimensional Einstein-Yang-Mills theory, with implications for cosmology.

Contribution

It introduces a novel interpretation of compactification as a topological defect and demonstrates a vortex solution in a higher-dimensional EYM framework.

Findings

A vortex solution in the effective Abelian gauge-Higgs theory.

The universe may be confined within a vortex in higher-dimensional space.

Connection to instanton-induced compactification and cosmological implications.

Abstract

An interpretation is suggested that a spontaneous compactification of space-time can be regarded as a topological defect in a higher-dimensional Einstein-Yang-Mills (EYM) theory. We start with $D$-dimensional EYM theory in our present analysis. A compactification leads to a $D-2$ dimensional effective action of Abelian gauge-Higgs theory. We find a "vortex" solution in the effective theory. Our universe appears to be confined in a center of a "vortex", which has $D-4$ large dimensions. In this paper we show an example with $SU(2)$ symmetry in the original EYM theory, and the resulting solution is found to be equivalent to the "instanton-induced compactification". The cosmological implication is also mentioned.