Stable exponential cosmological solutions with three different Hubble-like parameters in EGB model with a Λ -term

We consider a D-dimensional Einstein-Gauss-Bonnet model with a cosmological term Λ and two non-zero constants: α1 and α2. We restrict the metrics to be diagonal ones and study a class of solutions with exponential time dependence of three scale factors, governed by three non-coinciding Hubble-like parameters: H≠ 0 , h1 and h2, obeying mH+ k1h1+ k2h2≠ 0 and corresponding to factor spaces of dimensions m> 1 , k1> 1 and k2> 1 , respectively (D= 1 + m+ k1+ k2). We analyse two cases: i) m< k1< k2 and ii) 1 < k1= k2= k, k≠ m. We show that in both cases the solutions exist if α= α2/ α1> 0 and αΛ > 0 satisfies 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. For m> 3 the case i) contains a subclass of solutions describing an exponential expansion of 3-dimensional subspace with Hubble parameter H> 0 and zero variation of the effective gravitational constant G. The case H= 0 is also considered. © 2020, The Author(s).