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

TL;DR

This paper finds and analyzes stable exponential cosmological solutions with two factor spaces in a higher-dimensional Einstein-Gauss-Bonnet model including a cosmological constant, focusing on stability and gravitational constant variation.

Contribution

It presents exact exponential solutions with two scale factors in a $(1+m+2)$-dimensional EGB model and proves their stability under certain conditions, including small variations of G.

Findings

Stable solutions exist under specific parameter restrictions.

A subclass with minimal G variation is identified and shown to be stable.

Explicit conditions for stability are derived.

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 $h \neq H$, 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.