Exponential cosmological solutions with two factor spaces in EGB model with Λ=0 revisited

• Published in: The European physical journal. C, Particles and fields Vol. 79; no. 10
• Main Authors: Ivashchuk, V. D., Kobtsev, A. A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2019
• Subjects: Astronomy; Astrophysics and Cosmology; Elementary Particles; Hadrons; Heavy Ions; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; String Theory
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-019-7329-8

We study exact cosmological solutions in D -dimensional Einstein–Gauss–Bonnet model (with zero cosmological term) governed by two non-zero constants: α 1 and α 2 . We deal with exponential dependence (in time) of two scale factors governed by Hubble-like parameters H > 0 and h , which correspond to factor spaces of dimensions m > 2 and l > 2 , respectively, and D = 1 + m + l . We put h ≠ H and m H + l h ≠ 0 . We show that for α = α 2 / α 1 > 0 there are two (real) solutions with two sets of Hubble-like parameters: ( H 1 , h 1 ) and ( H 2 , h 2 ) , which obey: h 1 / H 1 < - m / l < h 2 / H 2 < 0 , while for α < 0 the (real) solutions are absent. We prove that the cosmological solution corresponding to ( H 2 , h 2 ) is stable in a class of cosmological solutions with diagonal metrics, while the solution corresponding to ( H 1 , h 1 ) is unstable. We present several examples of analytical solutions, e.g. stable ones with small enough variation of the effective gravitational constant G , for ( m , l ) = ( 9 , l > 2 ) , ( 12 , 11 ) , ( 11 , 16 ) , ( 15 , 6 ) .