Exponential cosmological solutions with two factor spaces in EGB model with Λ = 0 revisited

We study exact cosmological solutions in D-dimensional Einstein–Gauss–Bonnet model (with zero cosmological term) governed by two non-zero constants: α1 and α2. We deal with exponential dependence (in time) of two scale factors governed by Hubble-like parameters H> 0 and h, which correspond to factor spaces of dimensions m> 2 and l> 2 , respectively, and D= 1 + m+ l. We put h≠ H and mH+ lh≠ 0. We show that for α= α2/ α1> 0 there are two (real) solutions with two sets of Hubble-like parameters: (H1, h1) and (H2, h2) , which obey: h1/ H1< - m/ l< h2/ H2< 0 , while for α< 0 the (real) solutions are absent. We prove that the cosmological solution corresponding to (H2, h2) is stable in a class of cosmological solutions with diagonal metrics, while the solution corresponding to (H1, h1) is unstable. We present several examples of analytical solutions, e.g. stable ones with small enough variation of the effective gravitational constant G, for (m, l) = (9 , l> 2) , (12 , 11) , (11 , 16) , (15 , 6). © 2019, The Author(s)