Stable exponential cosmological solutions with zero variation of G in the Einstein–Gauss–Bonnet model with a Λ -term

A D-dimensional gravitational model with a Gauss–Bonnet term and the cosmological term Λ is considered. By assuming diagonal cosmological metrics, we find, for a certain fine-tuned Λ , 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) ≠ (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. © 2017, The Author(s).