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

• Main Authors: V. D. Ivashchuk, A. A. Kobtsev
• Format: Article
• Language: English
• Published: SpringerOpen 2019-10-01
• Series: European Physical Journal C: Particles and Fields
• Online Access: http://link.springer.com/article/10.1140/epjc/s10052-019-7329-8
• ISSN: 1434-6044; 1434-6052

Abstract We study exact cosmological solutions in D-dimensional Einstein–Gauss–Bonnet model (with zero cosmological term) governed by two non-zero constants: $$\alpha _1$$ α1 and $$\alpha _2$$ α2 . We deal with exponential dependence (in time) of two scale factors governed by Hubble-like parameters $$H >0$$ H>0 and h, which correspond to factor spaces of dimensions $$m >2$$ m>2 and $$l > 2$$ l>2 , respectively, and $$D = 1 + m + l$$ D=1+m+l . We put $$h \ne H$$ h≠H and $$mH + l h \ne 0$$ mH+lh≠0 . We show that for $$\alpha = \alpha _2/\alpha _1 > 0$$ α=α2/α1>0 there are two (real) solutions with two sets of Hubble-like parameters: $$(H_1, h_1)$$ (H1,h1) and $$(H_2, h_2)$$ (H2,h2) , which obey: $$ h_1/ H_1< - m/l< h_2/ H_2 < 0$$ h1/H1<-m/l<h2/H2<0 , while for $$\alpha < 0$$ α<0 the (real) solutions are absent. We prove that the cosmological solution corresponding to $$(H_2, h_2)$$ (H2,h2) is stable in a class of cosmological solutions with diagonal metrics, while the solution corresponding to $$(H_1, h_1)$$ (H1,h1) is unstable. We present several examples of analytical solutions, e.g. stable ones with small enough variation of the effective gravitational constant G, for $$(m, l) = (9, l >2), (12, 11), (11,16), (15, 6)$$ (m,l)=(9,l>2),(12,11),(11,16),(15,6) .