On stability of exponential cosmological solutions with non-static volume factor in the Einstein-Gauss-Bonnet model

TL;DR

This paper investigates the stability of exponential cosmological solutions with non-static volume factors in a higher-dimensional Einstein-Gauss-Bonnet model, identifying conditions for stability based on the sum of expansion rates.

Contribution

It provides a stability analysis for exponential solutions with non-static volume factors in Einstein-Gauss-Bonnet gravity, including specific conditions and examples of stable solutions.

Findings

Solutions with positive volume expansion rate are stable.

Solutions with negative volume expansion rate are unstable.

Certain stable solutions with zero variation of gravitational constant are identified.

Abstract

A (n+1)-dimensional gravitational model with Gauss-Bonnet term and cosmological constant term is considered. When ansatz with diagonal cosmological metrics is adopted, the solutions with exponential dependence of scale factors: a_i ~ exp( v^i t), i = 1, ..., n, are analysed for n > 3. We study the stability of the solutions with non-static volume factor, i.e. if K(v) = \sum_{k = 1}^{n} v^k \neq 0. We prove that under certain restriction R imposed solutions with K(v) > 0 are stable while solutions with K(v) < 0 are unstable. Certain examples of stable solutions are presented. We show that the solutions with v^1 = v^2 = v^3 = H > 0 and zero variation of the effective gravitational constant are stable if the restriction R is obeyed.