Stable exponential cosmological solutions with zero variation of G and three different Hubble-like parameters in the Einstein–Gauss–Bonnet model with a $$\Lambda $$ Λ -term

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.

Stable exponential cosmological solutions with three factor spaces of dimensions m = 3, k1 = k and k2 = k in the Einstein–Gauss–Bonnet model with a Λ-term

“…As it was proved in [26] by using results of ref. [27] (see also [8]), the exponential solutions with v from (3.1) and k 1 > 1, k 1 > 2 are stable if and only if…”

“…It was shown in ref. [26] that the set of (n + 1) polynomial equations (2.21), (2.22) with ansatz (3.1) and restrictions (3.3) imposed is reduced to a set of fourth, second and first order polynomial equations, accordingly:…”

Exponential Cosmological Solutions with Three Different Hubble-Like Parameters in (1 + 3 + k1 + k2)-Dimensional EGB Model with a Λ-Term

“…[20], the set of (n + 1) polynomial equations (2.4), (2.5), under ansatz (2.7) and restrictions (2.10) imposed, was reduced in ref. [29] to a set of three polynomial equations of fourth, second and first orders, respectively:…”

“…We single out (for both cases i) and ii)) the subclasses of stable and non-stable solutions. In the first case i) we consider as an example 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 [29].We note that earlier the ref.[30] was dealing with exponential cosmological solutions in the EGB model (with a Λ-term) with two non-coinciding Hubble parameters H > 0 and h obeying S 1 = 3H + lh 1 = 0 and corresponding to 3-and l-dimensional factor spaces (l > 1) in the EGB model with a Λ-term. In this case there were two sets of solutions obeying: a) α > 0, Λ < α −1 λ + (l) and b) α < 0, Λ > |α|λ − (l), with λ ± (l) > 0.…”

“…We single out (for both cases i) and ii)) the subclasses of stable and non-stable solutions. In the first case i) we consider as an example 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 [29].…”