Stable exponential cosmological solutions with 3- and l-dimensional factor spaces in the Einstein-Gauss-Bonnet model with a [Formula omitted]-term

• Published in: The European physical journal. C, Particles and fields Vol. 78; no. 2
• Main Authors: Ivashchuk, V. D, Kobtsev, A. A
• Format: Journal Article
• Language: English
• Published: Springer 03.02.2018
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-018-5591-9

A D-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term [Formula omitted] is studied. We assume the metrics to be diagonal cosmological ones. For certain fine-tuned [Formula omitted], we find a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters [Formula omitted] and h, corresponding to factor spaces of dimensions 3 and [Formula omitted], respectively and [Formula omitted]. The fine-tuned [Formula omitted] depends upon the ratio [Formula omitted], l and the ratio [Formula omitted] of two constants ( [Formula omitted] and [Formula omitted]) of the model. For fixed [Formula omitted] and [Formula omitted] the equation [Formula omitted] is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals (the example [Formula omitted] 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.