https://doi.org/10.1140/epjc/s10052-018-5591-9
Regular Article - Theoretical Physics
Stable exponential cosmological solutions with 3- and l-dimensional factor spaces in the Einstein–Gauss–Bonnet model with a 
-term
1
Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., Moscow, 117198, Russian Federation
2
Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya St., Moscow, 119361, Russian Federation
3
Institute for Nuclear Research, RAS, Troitsk, Moscow, 108840, Russian Federation
* e-mail: ivashchuk@mail.ru
Received:
29
December
2017
Accepted:
21
January
2018
Published online:
3
February
2018
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 
and h, corresponding to factor spaces of dimensions 3 and 
, respectively and 
. The fine-tuned 
depends upon the ratio 
, l and the ratio 
of two constants (
and 
) of the model. For fixed 
and the equation 
is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals (the example 
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.
© The Author(s), 2018
