Stable exponential cosmological solutions with two factor spaces in the Einstein-Gauss-Bonnet model with a $\Lambda$-term

Abstract

We study $D$-dimensional Einstein-Gauss-Bonnet gravitational model including the Gauss-Bonnet term and the cosmological term $\Lambda$. We find a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters $H>0$ and $h$, corresponding to factor spaces of dimensions $m>2$ and $l>2$, respectively. These solutions contain a fine-tuned $\Lambda =\Lambda (x,m,l,\alpha )$, which depends upon the ratio $h/H=x$, dimensions of factor spaces $m$ and $l$, and the ratio $\alpha ={\alpha }_2/{\alpha }_1$ of two constants (${\alpha }_2$ and ${\alpha }_1$) of the model. The master equation $\Lambda (x,m,l,\alpha )=\Lambda$ is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals. The explicit solution for $m=l$ is presented in Appendix. Imposing certain restrictions on $x$, we prove the stability of the solutions in a class of cosmological solutions with diagonal metrics. We also consider a subclass of solutions with small enough variation of the effective gravitational constant $G$ and show the stability of all solutions from this subclass.

37 pages, Latex, 8 figures, 42 references. One typo in eq. (3.77) is eliminated, one phrase in Introduction and the last reference are omitted. To be published in GERG

References in corpus (12)

• Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• The Lovelock Black Holes
• Accelerating Cosmologies in the Einstein-Gauss-Bonnet Theory with Dilaton
• Stationary vs. singular points in an accelerating FRW cosmology derived from six-dimensional Einstein-Gauss-Bonnet gravity
• Cosmic acceleration with a negative cosmological constant in higher dimensions
• On stability of exponential cosmological solutions with non-static volume factor in the Einstein-Gauss-Bonnet model
• Models of G time variations in diverse dimensions
• Cosmological dynamics of spatially flat Einstein-Gauss-Bonnet models in various dimensions: High-dimensional $\Lambda$-term case
• On stable exponential cosmological solutions in the EGB model with a $\Lambda$-term in dimensions D = 5,6,7,8
• On stable exponential solutions in Einstein-Gauss-Bonnet cosmology with zero variation of G
• Stable exponential cosmological solutions with zero variation of $G$ and three different Hubble-like parameters in the Einstein-Gauss-Bonnet model with a $\Lambda$-term
• Realistic Compactification Models in Einstein-Gauss-Bonnet Gravity

Cited by in corpus (6)

• Splitting into two isotropic subspaces as a result of cosmological evolution in Einstein-Gauss-Bonnet gravity
• Stable exponential cosmological solutions with three different Hubble-like parameters in EGB model with a $\Lambda$-term
• Cosmological Models in Lovelock Gravity: An Overview of Recent Progress
• Stable exponential cosmological solutions with three factor spaces in $(1+3+3+k)$-dimensional Einstein-Gauss-Bonnet model with a $\Lambda$-term
• Stable exponential cosmological solutions with three factor spaces of dimensions $m=3$, $k_1=k$ and $k_2=k$ in the Einstein-Gauss-Bonnet model with a $\Lambda$-term
• On the Properties of the Power-Law Cosmological Solutions in Lovelock Gravity