Stable exponential cosmological solutions with 3- and l-dimensional factor spaces in the Einstein–Gauss–Bonnet model with a $$\Lambda $$ Λ -term

Abstract

A D-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term is studied. We assume the metrics to be diagonal cosmological ones. For certain fine-tuned , we find a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters H > 0 and h, corresponding to factor spaces of dimensions 3 and l > 2, respectively and D = 1 + 3 + l. The fine-tuned = (x, l, α) depends upon the ratio h/H = x, l and the ratio α = α 2 /α 1 of two constants (α 2 and α 1 ) of the model. For fixed , α and l > 2 the equation (x, l, α) = is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals (the example l = 3 is presented). For certain restrictions on x we prove the stability of the solutions in a class of cosmological solutions with diagonal metrics. A subclass of solutions with small enough variation of the effective gravitational constant G is considered. It is shown that all solutions from this subclass are stable.

Cosmological solutions in Einstein–Gauss–Bonnet gravity with static curved extra dimensions

“…Let us also note that for a flat internal space (γ D = 0) the solutions under consideration do exist for α < 0 and = −3/(2α) > 0 and are stable for D > 2 [61] and D = 2 [62].…”

Exponential cosmological solutions in Einstein-Gauss-Bonnet gravity with two subspaces: general approach

“…Note added: after this manuscript was submitted to arXiv, we became aware of previously published paper [53], where same problem was considered. The case with p = 3 was considered in [37] while q = 2 case in [38]. We would like to thank V.D.…”

“…We have also described the general scheme for finding all possible exponential solutions in arbitrary dimensions and with arbitrary Lovelock contributions taken into account in [33]. Deeper investigation revealed that not all of the solutions found in [33] are stable [34]; see also [35] for more general approach to the stability of exponential solutions in EGB gravity and [36][37][38] for some particular cases.…”

Exact (1 + 3 + 6)-Dimensional Cosmological-Type Solutions in Gravitational Model with Yang–Mills Field, Gauss–Bonnet Term and Λ Term

“…Using results of Ref. [22,24] we obtain that cosmological solutions under consideration obeying x = h/H = x i , i = a, c, d, where x a = 1,…”

“…The evolution of the 6-dimensional internal factor space is described by the Hubble-like parameter h. It follows from Ref. [22,24] (for a more general splitting scheme see paper by Chirkov, Pavluchenko and Toporensky [18]) that if we consider Hubble-like parameters H and h obeying two restrictions imposed…”