Stable exponential cosmological solutions with zero variation of G in the Einstein\u2013Gauss\u2013Bonnet model with a Lambda -term

Abstract

A D-dimensional gravitational model with a Gauss–Bonnet term and the cosmological term Lambda is considered. By assuming diagonal cosmological metrics, we find, for a certain fine-tuned Lambda , a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters H >0 and h < 0, corresponding to factor spaces of dimensions m > 3 and l > 1, respectively, with (m,l) ne (6,6), (7,4), (9,3) and D = 1 + m + l. Any of these solutions describes an exponential expansion of three-dimensional subspace with Hubble parameter H and zero variation of the effective gravitational constant G. We prove the stability of these solutions in a class of cosmological solutions with diagonal metrics.