Spontaneous decompactification

TL;DR

This paper reviews the instability of our universe due to positive vacuum energy causing extra dimensions to decompactify, exploring the dynamics and potential mechanisms for compactification and decompactification in higher-dimensional cosmology.

Contribution

It provides an overview of the decompactification process, analyzes fixed-point solutions for different curvatures, and discusses mechanisms for transitioning between higher-dimensional and four-dimensional cosmologies.

Findings

Decompactification can occur via quantum tunneling or thermal fluctuations.

Fixed-point solutions govern the expansion into higher dimensions.

A possible mechanism for compactification to four-dimensional de Sitter space is outlined.

Abstract

Positive vacuum energy together with extra dimensions of space imply that our four-dimensional Universe is unstable, generically to decompactification of the extra dimensions. Either quantum tunneling or thermal fluctuations carry one past a barrier into the decompactifying regime. We give an overview of this process, and examine the subsequent expansion into the higher- dimensional geometry. This is governed by certain fixed-point solutions of the evolution equations, which are studied for both positive and negative spatial curvature. In the case where there is a higher-dimensional cosmological constant, we also outline a possible mechanism for compactification to a four-dimensional de Sitter cosmology.