No abstract

We consider a D-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term . We restrict the metrics to diagonal cosmological ones and find for certain a class of solutions with exponential time dependence of three scale factors, governed by three non-coinciding Hubble-like parameters H > 0, h 1 and h 2 , corresponding to factor spaces of dimensions m > 2, k 1 > 1 and k 2 > 1, respectively, with k 1 = k 2 and D = 1 + m + k 1 + k 2 . Any of these solutions describes an exponential expansion of 3d subspace with Hubble parameter H and zero variation of the effective gravitational constant G. We prove the stability of these solutions in a class of cosmological solutions with diagonal metrics.

We consider a D-dimensional Einstein-Gauss-Bonnet model with a cosmological term and two non-zero constants: α 1 and α 2. 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, h 1 and h 2 , obeying m H + k 1 h 1 + k 2 h 2 = 0 and corresponding to factor spaces of dimensions m > 1, k 1 > 1 and k 2 > 1, respectively (D = 1 + m + k 1 + k 2). We analyse two cases: i) m < k 1 < k 2 and ii) 1 < k 1 = k 2 = k, k = m. We show that in both cases the solutions exist if α = α 2 /α 1 > 0 and α > 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.

A D-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term is considered. By assuming diagonal cosmological metrics, we find, for a certain fine-tuned , a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters H > 0 and h < 0, corresponding to factor spaces of dimensions m > 3 and l > 1, respectively, with (m, l) = (6, 6), (7, 4), (9, 3) and D = 1+m +l. Any of these solutions describes an exponential expansion of threedimensional subspace with Hubble parameter H and zero variation of the effective gravitational constant G. We prove the stability of these solutions in a class of cosmological solutions with diagonal metrics.

We deal with Einstein-Gauss-Bonnet model in dimension D with a Λ-term. We obtain three stable cosmological solutions with exponential behavior (in time) of three scale factors corresponding to subspaces of dimensions (l 0 , l 1 , l 2 ) = (3, 4, 4), (3, 3, 2), (3, 4, 3) and D = 12, 9, 11, respectively. Any solution may describe an exponential expansion of 3-dimensional subspace governed by Hubble parameter H. Two of them may also describe a small enough variation of the effective gravitational constant G (in Jordan frame) for certain values of Λ.