Spontaneous Compactification to Robertson-Walker Universe Due To Dynamical Torsion

TL;DR

This paper explores how dynamical torsion in higher-dimensional gravity can lead to spontaneous compactification of extra dimensions into a Robertson-Walker universe, with stable minima occurring at zero torsion.

Contribution

It demonstrates that in multidimensional gravity with torsion and the Gauss-Bonnet term, stable compactification can occur without torsion, revealing a new mechanism for dimensional reduction.

Findings

Stable minima of the potential correspond to compactified extra dimensions.

The minima occur at zero torsion, indicating torsion-free stable configurations.

The model identifies parameter conditions for spontaneous compactification.

Abstract

We investigate multidimensional gravity with the Gauss-Bonnet term and with torsion on the space of extra dimensions chosen to be the group manifold of a simple Lie group. We take the Robertson-Walker ansatz for the 4-dimensional space-time and study the potential of a dilaton and torsion fields. It is shown that for certain values of the parameters of the initial theory the potential has classically stable minima, corresponding to the spontaneous compactification of the extra dimensions. However, these minima have zero torsion.