Some aspects of the cosmological dynamics in Einstein-Gauss-Bonnet gravity

TL;DR

This paper investigates the stability of cosmological solutions in Einstein-Gauss-Bonnet gravity, revealing that stable exponential expansion with negatively curved extra dimensions cannot coexist with stable compactification solutions of positively curved extra dimensions.

Contribution

It demonstrates the instability of positive curvature compactification solutions in certain stable exponential cosmological scenarios within Einstein-Gauss-Bonnet gravity.

Findings

Stable exponential solutions with negative curvature are incompatible with positive curvature compactification.

Two-stage cosmological evolution scenario is not realizable with positive curvature.

Introduces a new parametrization for solutions in models with arbitrary constant curvature.

Abstract

We study some aspects of dynamical compactification scenario where stabilisation of extra dimensions occurs due to presence the Gauss-Bonnet term and non-zero spatial curvature. In the framework of the model under consideration there exists two-stages scenario of evolution of a Universe: on the first stage, the space evolves from a totally anisotropic state to the state with 3-dimensional (corresponding to our "real", world) expanding and $D$-dimensional contracting isotropic subspaces; on the second stage, constant curvature of extra dimensions begins to play role and provide compactification of extra dimensions. It is already known that such a scenario is realizable when constant curvature of extra dimensions is negative. Here we show that a range of coupling constants for which exponential solutions with 3-dimensional expanding and $D$-dimensional contracting isotropic subspaces are stable is located in a zone where compactification solutions with positively curved extra space are unstable, so that two-stage scenario analogous to the one described above is \emph{not} realizable. Also we study "nearly-Friedmann", regime for the case of arbitrary constant curvature of extra dimensions and describe new parametrization of the general solution for the model under consideration which provide elegant way of describing areas of existence over parameters space.