Exponential cosmological solutions with three different Hubble-like parameters in (1+3+k1 +k2)-dimensional EGB model with a Λ-term

A D-dimensional Einstein-Gauss-Bonnet model with a cosmological term Λ, governed by two non-zero constants: α1 and α2, is considered. By restricting the metrics to diagonal ones, we study a class of solutions with the exponential time dependence of three scale factors, governed by three non-coinciding Hubble-like parameters: H > 0, h1, and h2, obeying 3H + k1h1 + k2h2 ≠ 0 and corresponding to factor spaces of dimensions: 3, k1 > 1, and k2 > 1, respectively, with D = 4+k1 +k2. The internal flat factor spaces of dimensions k1 and k2 have non-trivial symmetry groups, which depend on the number of compactified dimensions. Two cases: (i) 3 < k1 < k2 and (ii) 1 < k1 = k2 = k, k ≠ 3, are analyzed. It is shown that in both cases, the solutions exist if α = α2/α1 > 0 and αΛ > 0 obey certain restrictions, e.g., upper and lower bounds. In Case (ii), explicit relations for exact solutions are found. In both cases, the subclasses of stable and non-stable solutions are singled out. Case (i) contains a subclass of solutions describing an exponential expansion of 3d subspace with Hubble parameter H > 0 and zero variation of the effective gravitational constant G. © 2020 by the authors.