Dynamical compactification in Einstein-Gauss-Bonnet gravity from geometric frustration

TL;DR

This paper demonstrates that in Einstein-Gauss-Bonnet gravity, negative curvature of extra dimensions leads to realistic dynamical compactification without fine-tuning, with stability improving as the number of extra dimensions increases.

Contribution

It reveals a natural dynamical compactification mechanism in Einstein-Gauss-Bonnet gravity driven by geometric frustration, avoiding fine-tuning of coupling constants.

Findings

Extra dimensions stabilize with negative curvature.

No fine-tuning needed for realistic compactification.

Stability improves with more extra dimensions.

Abstract

In this paper we study dynamical compactification in Einstein-Gauss-Bonnet gravity from arbitrary dimension for generic values of the coupling constants. We showed that, when the curvature of the extra dimensional space is negative, for any value of the spatial curvature of the four dimensional space-time one obtains a realistic behavior in which for asymptotic time both the volume of the extra dimension and expansion rate of the four dimensional space-time tend to a constant. Remarkably, this scenario appears within the open region of parameters space for which the theory does not admit any maximally symmetric (4+D)- dimensional solution, which gives to the dynamical compactification an interpretation as geometric frustration. In particular there is no need to fine-tune the coupling constants of the theory so that the present scenario does not violate "naturalness hypothesis". Moreover we showed that with increase of the number of extra dimensions the stability properties of the solution are increased.