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: α 1 and α 2 , 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 , h 1 , and h 2 , obeying 3 H + k 1 h 1 + k 2 h 2 ≠ 0 and corresponding to factor spaces of dimensions: 3, k 1 > 1 , and k 2 > 1 , respectively, with D = 4 + k 1 + k 2 . The internal flat factor spaces of dimensions k 1 and k 2 have non-trivial symmetry groups, which depend on the number of compactified dimensions. Two cases: (i) 3 0 and α Λ > 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 3 d subspace with Hubble parameter H > 0 and zero variation of the effective gravitational constant G.

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