On cosmological-type solutions in multi-dimensional model with Gauss-Bonnet term

Abstract

A (n + 1)-dimensional Einstein-Gauss-Bonnet (EGB) model is considered. For diagonal cosmological-type metrics, the equations of motion are reduced to a set of Lagrange equations. The effective Lagrangian contains two "minisuperspace" metrics on R^n. The first one is the well-known 2-metric of pseudo-Euclidean signature and the second one is the Finslerian 4-metric that is proportional to n-dimensional Berwald-Moor 4-metric. When a "synchronous-like" time gauge is considered the equations of motion are reduced to an autonomous system of first-order differential equations. For the case of the "pure" Gauss-Bonnet model, two exact solutions with power-law and exponential dependence of scale factors (with respect to "synchronous-like" variable) are obtained. (In the cosmological case the power-law solution was considered earlier in papers of N. Deruelle, A. Toporensky, P. Tretyakov and S. Pavluchenko.) A generalization of the effective Lagrangian to the Lowelock case is conjectured. This hypothesis implies existence of exact solutions with power-law and exponential dependence of scale factors for the "pure" Lowelock model of m-th order.

24 pages, Latex, typos are eliminated

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• Friedmann dynamics recovered from compactified Einstein-Gauss-Bonnet cosmology
• Cosmological dynamics of spatially flat Einstein-Gauss-Bonnet models in various dimensions: Low-dimensional $\Lambda$-term case
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• Inhomogeneous compact extra dimensions and de Sitter cosmology
• Classical evolution of subspaces
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• Some aspects of the cosmological dynamics in Einstein-Gauss-Bonnet gravity
• Dynamic compactification with stabilized extra dimensions in cubic Lovelock gravity
• Stable exponential cosmological solutions with zero variation of G in the Einstein-Gauss-Bonnet model with a Lambda-term
• Splitting into two isotropic subspaces as a result of cosmological evolution in Einstein-Gauss-Bonnet gravity
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• Examples of stable exponential cosmological solutions with three factor spaces in EGB model with a $\Lambda$-term
• Anisotropic cosmological dynamics in Einstein-Gauss-Bonnet gravity: an example of dynamical compactification in 7+1 dimensions
• Realistic compactification in spatially flat vacuum cosmological models in cubic Lovelock gravity: Low-dimensional case
• Stable exponential cosmological solutions with three different Hubble-like parameters in EGB model with a $\Lambda$-term
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• Spontaneous symmetry breaking as a result of extra dimensions compactification
• Evolution of sub-spaces at high and low energies
• Exponential cosmological solutions with two factor spaces in EGB model with $\Lambda =0$ revisited
• Cosmological Models in Lovelock Gravity: An Overview of Recent Progress
• On non-exponential cosmological solutions with two factor spaces of dimensions $m$ and $1$ in the Einstein-Gauss-Bonnet model with a $\Lambda$-term
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• 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
• 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