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

In this paper we study dynamical compactification in Einstein-Gauss-Bonnet gravity from an arbitrary dimension for generic values of the coupling constants. We show 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 the "naturalness hypothesis." Moreover we show that with an increase of the number of extra dimensions the stability properties of the solution are increased.