On anisotropic Gauss-Bonnet cosmologies in (<Emphasis Type="Italic">n</Emphasis> + 1) dimensions,governed by an <Emphasis Type="Italic">n</Emphasis>-dimensional Finslerian 4-metric

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) are presented. (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 nontrivial 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 .