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

Abstract

We study some aspects of dynamical compactification scenario where stabilization of extra dimensions occurs due to the presence of Gauss–Bonnet term and nonzero spatial curvature. In the framework of the model under consideration, there exists two-stages scenario of evolution of a Universe: in the first stage, the space evolves from a totally anisotropic state to the state with three-dimensional (corresponding to our “real” world) expanding and [Formula: see text]-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 three-dimensional expanding and [Formula: see text]-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 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.