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

Abstract

We study exact cosmological solutions in $D$-dimensional Einstein-Gauss-Bonnet model (with zero cosmological term) governed by two non-zero constants: ${\alpha }_1$ and ${\alpha }_2$. 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 $h\ne H$ and $mH+lh\ne 0$. We show that for $\alpha ={\alpha }_2/{\alpha }_1>0$ 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 $\alpha <0$ 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 $(m,l)=(9,l>2),(12,11),(11,16),(15,6)$.

arXiv comment21 pages, Latex, 3 figures, revised version, Appendix is added

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