On stable exponential solutions in Einstein–Gauss–Bonnet cosmology with zero variation of G

Abstract

A D-dimensional gravitational model with a Gauss–Bonnet term and the cosmological constant Λ is considered. Assuming diagonal cosmological metrics, we find, for certain Λ > 0, new examples of solutions with an exponential time dependence of two scale factors, governed by two Hubble-like parameters H > 0 and h < 0, corresponding to submanifolds of dimensions m and l, respectively, with (m, l) = (4, 2), (5, 2), (5, 3), (6, 7), (7, 5), (7, 6) and D = 1 + m + l. Any of these solutions describes an exponential expansion of our 3-dimensional factor space with the Hubble parameter H and zero variation of the effective gravitational constant G. We also prove the stability of these solutions in the class of cosmological solutions with diagonal metrics.