On anisotropic Gauss-Bonnet cosmologies in (n+1) dimensions, governed by an n-dimensional Finslerian 4-metric

Abstract

The (n +1)-dimensional Einstein-Gauss-Bonnet (EGB) model is considered. For diagonal cosmological metrics, the equations of motion are written as a set of Lagrange equations with the effective Lagrangian containing two "minisuperspace" metrics on R^n: a 2-metric of pseudo-Euclidean signature and a Finslerian 4-metric proportional to the n-dimensional Berwald-Moor 4-metric. For the case of the "pure" Gauss-Bonnet model, two exact solutions are presented, those with power-law and exponential dependences of the scale factors (w.r.t. the synchronous time variable). (The power-law solution was considered earlier by N. Deruelle, A. Toporensky, P. Tretyakov, and S. Pavluchenko.) In the case of EGB cosmology, it is shown that for any non-trivial solution with an exponential dependence of scale factors, a_i(τ) = A_i exp(v^i τ), there are no more than three different numbers among v^1, ..., v^n.

14 pages, Latex, refs. are added, typos are eliminated

References in corpus (13)

• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• 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
• On cosmological-type solutions in multi-dimensional model with Gauss-Bonnet term
• General features of Bianchi-I cosmological models in Lovelock gravity
• Brane world corrections to Newton's law
• A note on differences between (4+1)- and (5+1)-dimensional anisotropic cosmology in the presence of the Gauss-Bonnet term
• Sp-brane accelerating cosmologies
• On billiard approach in multidimensional cosmological models
• Electric S-brane solutions corresponding to rank-2 Lie algebras: acceleration and small variation of G
• Construction of the pseudo Riemannian geometry on the base of the Berwald-Moor geometry

Cited by in corpus (26)

• On cosmological-type solutions in multi-dimensional model with Gauss-Bonnet term
• On stability of exponential cosmological solutions with non-static volume factor in the Einstein-Gauss-Bonnet model
• Cosmological dynamics in higher-dimensional Einstein-Gauss-Bonnet gravity
• Friedmann dynamics recovered from compactified Einstein-Gauss-Bonnet cosmology
• Autonomous Dynamical System of Einstein-Gauss-Bonnet Cosmologies
• On stable exponential cosmological solutions in the EGB model with a $\Lambda$-term in dimensions D = 5,6,7,8
• Note on properties of exact cosmological solutions in Lovelock gravity
• On stable exponential solutions in Einstein-Gauss-Bonnet cosmology with zero variation of G
• On exponential cosmological type solutions in the model with Gauss-Bonnet term and variation of gravitational constant
• 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
• Stable exponential cosmological solutions with two factor spaces 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
• Anisotropic cosmological dynamics in Einstein-Gauss-Bonnet gravity: an example of dynamical compactification in 7+1 dimensions
• On stability of power-law solution in multidimensional Gauss-Bonnet cosmology
• Stable exponential cosmological solutions with three different Hubble-like parameters in EGB model with a $\Lambda$-term
• Spontaneous symmetry breaking as a result of extra dimensions compactification
• Cosmological Models in Lovelock Gravity: An Overview of Recent Progress
• Exponential cosmological solutions with two factor spaces in EGB model with $\Lambda =0$ revisited
• On non-exponential cosmological solutions with two factor spaces of dimensions $m$ and $1$ in the Einstein-Gauss-Bonnet model with a $\Lambda$-term
• Exact $(1+3+6)$-dimensional cosmological-type solutions in gravitational model with Yang-Mills field, Gauss-Bonnet term and $\Lambda$-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
• Examples of exact exponential cosmological solutions with three isotropic subspaces in the Einstein-Gauss-Bonnet gravity
• 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