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

• Published in: arXiv.org
• Main Author: Ivashchuk, V D
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 30.04.2010
• Subjects: Cosmology; Dependence; Equations of motion; Euclidean geometry; Euler-Lagrange equation; Mathematical models; Physics - General Relativity and Quantum Cosmology; Power law
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.0909.5462

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(\tau) = A_i exp(v^i \tau), there are no more than three different numbers among v^1, ..., v^n.