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

TL;DR

This paper explores (n+1)-dimensional Einstein-Gauss-Bonnet cosmologies with diagonal metrics, revealing exact power-law and exponential solutions, and demonstrating constraints on exponential scale factor rates in such models.

Contribution

It introduces a Finslerian 4-metric into the Einstein-Gauss-Bonnet framework and provides explicit solutions, extending previous work with new geometric insights.

Findings

Two exact solutions: power-law and exponential scale factors.

Exponential solutions have at most three distinct rates among scale factors.

The model incorporates a Finslerian 4-metric related to the Berwald-Moor 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(\tau) = A_i exp(v^i \tau), there are no more than three different numbers among v^1, ..., v^n.