Gauge Group and Topology Change

TL;DR

This paper explores how topology change in the early universe can be modeled using $G$-cobordism, showing that symmetry reduction and compactification processes are fundamental to the universe's evolution.

Contribution

It introduces the concept of $G$-cobordism to analyze topology change in the universe and links it to fiber bundle structures in Kaluza-Klein and Einstein-Yang-Mills theories.

Findings

Topology change involves symmetry reduction and dimension compactification.

$G$-manifolds serve as models for early universe topology transitions.

Results suggest fundamental processes drive the universe from high symmetry to current state.

Abstract

The purpose of this study is to examine the effect of topology change in the initial universe. In this study, the concept of $G$-cobordism is introduced to argue about the topology change of the manifold on which a transformation group acts. This $G$-manifold has a fiber bundle structure if the group action is free and is related to the spacetime in Kaluza-Klein theory or Einstein-Yang-Mills system. Our results revealed that fundamental processes of compactification in $G$-manifolds. In these processes, the initial high symmetry and multidimensional universe changes to present universe by the mechanism which lowers the dimensions and symmetries.