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

Abstract

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).