Stable Exponential Cosmological Type Solutions with Three Factor Spaces in EGB Model with a Λ-Term

Abstract

We study a D-dimensional Einstein–Gauss–Bonnet model which includes the Gauss–Bonnet term, the cosmological term Λ and two non-zero constants: α1 and α2. Under imposing the metric to be diagonal one, we find cosmological type solutions with exponential dependence of three scale factors in a variable u, governed by three non-coinciding Hubble-like parameters: H≠0, h1 and h2, obeying mH+k1h1+k2h2≠0, corresponding to factor spaces of dimensions m>1, k1>1 and k2>1, respectively, and depending upon sign parameter ε=±1, where ε=1 corresponds to cosmological case and ε=−1—to static one). We deal with two cases: (i) m<k1<k2 and (ii) 1<k1=k2=k, k≠m. We show that in both cases the solutions exist if εα=εα2/α1>0 and αΛ>0 satisfy certain (upper and lower) bounds. The solutions are defined up to solutions of a certain polynomial master equation of order four (or less), which may be solved in radicals. In case (ii), explicit solutions are presented. In both cases we single out stable and non-stable solutions as u→±∞. The case H=0 is also considered.