On stability of exponential cosmological solutions with non-static volume factor in the Einstein-Gauss-Bonnet model

Abstract

A (n+1)-dimensional gravitational model with Gauss-Bonnet term and cosmological constant term is considered. When ansatz with diagonal cosmological metrics is adopted, the solutions with exponential dependence of scale factors: a_i ~ exp( v^i t), i = 1, ..., n, are analysed for n > 3. We study the stability of the solutions with non-static volume factor, i.e. if K(v) = \sum_{k = 1}^{n} v^k \neq 0. We prove that under certain restriction R imposed solutions with K(v) > 0 are stable while solutions with K(v) < 0 are unstable. Certain examples of stable solutions are presented. We show that the solutions with v^1 = v^2 = v^3 = H > 0 and zero variation of the effective gravitational constant are stable if the restriction R is obeyed.

20 pages, no figures, LaTex; two Remarks (1 and 4) and 7 references are added

References in corpus (8)

• Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• Accelerating Cosmologies in the Einstein-Gauss-Bonnet Theory with Dilaton
• One-loop effective action for non-local modified Gauss-Bonnet gravity in de Sitter space
• 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
• A note on differences between (4+1)- and (5+1)-dimensional anisotropic cosmology in the presence of the Gauss-Bonnet term
• Models of G time variations in diverse dimensions
• Power-law anisotropic cosmological solution in 5+1 dimensional Gauss-Bonnet gravity

Cited by in corpus (15)

• Non-exotic matter wormholes in a trace of the energy-momentum tensor squared gravity
• Cosmological dynamics of spatially flat Einstein-Gauss-Bonnet models in various dimensions: Low-dimensional $\Lambda$-term case
• Separation of variables in Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in the Stackel spaces of type (1.1)
• 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
• Stable exponential cosmological solutions with zero variation of G in the Einstein-Gauss-Bonnet model with a Lambda-term
• Examples of stable exponential cosmological solutions with three factor spaces in EGB model with a $\Lambda$-term
• Spontaneous symmetry breaking as a result of extra dimensions compactification
• Exponential cosmological solutions with two factor spaces in EGB model with $\Lambda =0$ revisited
• Cosmological Models in Lovelock Gravity: An Overview of Recent Progress
• Exact $(1+3+6)$-dimensional cosmological-type solutions in gravitational model with Yang-Mills field, Gauss-Bonnet term and $\Lambda$-term
• On non-exponential cosmological solutions with two factor spaces of dimensions $m$ and $1$ in the Einstein-Gauss-Bonnet model with a $\Lambda$-term
• Stable exponential cosmological solutions with three factor spaces in $(1+3+3+k)$-dimensional Einstein-Gauss-Bonnet model with a $\Lambda$-term
• On the Properties of the Power-Law Cosmological Solutions in Lovelock Gravity
• 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