Einstein-Gauss-Bonnet gravity with extra dimensions

TL;DR

This paper explores a modified gravity theory with extra dimensions, showing how a specific quadratic curvature combination yields a 4D Horndeski scalar-tensor theory and discusses stabilizing extra dimensions.

Contribution

It demonstrates that a special quadratic curvature combination in higher dimensions leads to a 4D Horndeski scalar-tensor theory via dimensional reduction.

Findings

Special quadratic curvature terms produce a Horndeski scalar-tensor theory in 4D.

Conditions for stabilizing extra dimensions are analyzed.

The role of Gauss-Bonnet coupling in extra dimension stability is discussed.

Abstract

We consider a theory of modified gravity possessing d extra spatial dimensions with a maximally symmetric metric and a scale factor, whose (4+d)-dimensional gravitational action contains terms proportional to quadratic curvature scalars. Constructing the 4D effective field theory by dimensional reduction, we find that a special case of our action where the additional terms appear in the well-known Gauss-Bonnet combination is of special interest as it uniquely produces a Horndeski scalar-tensor theory in the 4D effective action. We further consider the possibility of achieving stabilised extra dimensions in this scenario, as a function of the number and curvature of extra dimensions, as well as the strength of the Gauss-Bonnet coupling. Further questions that remain to be answered such as the influence of matter-coupling are briefly discussed.