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

A (n+ 1) -dimensional gravitational model with Gauss–Bonnet term and a cosmological constant term is considered. When ansatz with diagonal cosmological metrics is adopted, the solutions with an exponential dependence of the scale factors, ai∼ exp (vit) , i= 1 , ⋯ , n, are analyzed for n> 3. We study the stability of the solutions with non-static volume factor, i.e. if K(v)=∑k=1nvk≠0. We prove that under a 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 v1= v2= v3= H> 0 and zero variation of the effective gravitational constant are stable if the restriction R is obeyed. © 2016, The Author(s).