On stable exponential cosmological solutions with two factor spaces in $(1+m+2)$-dimensional EGB model with $\Lambda$-term

Abstract

A $(m+3)$-dimensional Einstein-Gauss-Bonnet gravitational model including the Gauss-Bonnet term and the cosmological term $\Lambda$ is considered. Exact solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters $H>0$ and $h\ne H$, corresponding to factor spaces of dimensions $m>2$ and $l=2$, respectively, are found. Under certain restrictions on $x=h/H$, the stability of the solutions in a class of cosmological solutions with diagonal metrics is proved. A subclass of solutions with small enough variation of the effective gravitational constant $G$ is considered and the stability of all solutions from this subclass is shown.

24 pages, 3 figures, Latex, a section (on D=4) with corresponding references is omitted and 3 figures are replaced