Stable exponential cosmological solutions with zero variation of G and three different Hubble-like parameters in the Einstein–Gauss–Bonnet model with a $$\Lambda $$ Λ -term

Abstract

Abstract We consider a D-dimensional gravitational model with a Gauss–Bonnet term and the cosmological term $$\Lambda $$ Λ . We restrict the metrics to diagonal cosmological ones and find for certain $$\Lambda $$ Λ a class of solutions with exponential time dependence of three scale factors, governed by three non-coinciding Hubble-like parameters $$H >0$$ H > 0 , $$h_1$$ h 1 and $$h_2$$ h 2 , corresponding to factor spaces of dimensions $$m > 2$$ m > 2 , $$k_1 > 1$$ k 1 > 1 and $$k_2 > 1$$ k 2 > 1 , respectively, with $$k_1 \ne k_2$$ k 1 ≠ k 2 and $$D = 1 + m + k_1 + k_2$$ D = 1 + m + k 1 + k 2 . Any of these solutions describes an exponential expansion of 3d 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.