On anisotropic cosmological solutions in (n+ 1)-dimensional model with Gauss-Bonnet term governed by n-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 Lagrangian containing two “minisuperspace” metrics on R : a 2-metric of pseudo-Euclidean signature and a Finslerian 4-metric that is proportional to n-dimensional Berwald-Moor 4-metric. When a synchronous time variable 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 (w.r.t. synchronous time variable) are obtained. The first one was obtained earlier by A. Toporensky and P. Tretyakov for n = 5 (and verified for n = 6, 7).