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

Abstract

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