On Stability of Exponential Cosmological Type Solutions with Two Factor Spaces in the Einstein–Gauss–Bonnet Model with a Λ -Term

Abstract: We study a D-dimensional Einstein–Gauss–Bonnet gravitational model including the Gauss-Bonnet term and the cosmological constant Λ. We find a class of cosmological type solutions with exponential dependence of two scale factors on the variable u (either cosmological time or a spatial coordinate), governed by two Hubble-like parameters H = 0 and h, corresponding to factor spaces of dimensions m>2 and l>2, respectively, and depending on the sign parameter ε = ±1 (ε = 1 corresponds to cosmological solutions and ε = −1 to static ones). These solutions are governed by a certain master equation Λα = λ(x) and the restriction αε(x − x+)(x − x−)<0 (x− < x+ < 0) for the ratio h/H=x, where α = α2/α1 is the ratio of two constants of the model. The master equation is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals. Imposing certain restrictions on x, and we prove the stability of the solutions for u→±∞ in a certain class of cosmological solutions with diagonal metrics. © 2020, Pleiades Publishing, Ltd.