Lagrange aproach in (n+1)-dimensional "Einstein-Gauss-Bonnet" model and n-dimensional Berwald-Moor metric
2009jbv | V.D. Ivashchuk  // Center for Gravitation and Fundamental Metrology, VNIIMS, Moscow, Russia, Institute of Gravitation and Cosmology, Peoples Friendship University, Moscow, Russia, ivashchuk@mail.ru

A $(n +1)$-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 $\R^{n}$: a 2-metric of pseudo-Euclidean signature and Finslerian 4-metric that is proportional to $n$-dimensional Berwald-Moor 4-metric. For the case of synchronous time variable the equations of motion reduce to an autonomous system of first order differential equations. For the case of the ``pure'' Gauss-Bonnet model exact solutions with power-law and exponential dependence of scale factors (w.r.t. synchronous time variable) are presented. In the case of EGB cosmology, it is shown that for any non-trivial solution with exponential dependence of scale factors $a_i(\tau) = A_i \exp( v^i \tau)$ there are no more than three different numbers among $v^1,...,v^n$.

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