ИСТИНА

In the sixties of the last century Belinskii, Khalatnikov and Lifshitz (BKL) ascertained that Kasner solution being a general solution for a vacuum Bianchi I Universe becomes unstable in the case of metric with positive spatial curvature (belonging to Bianchi IX class) and is replaced by a complicated sequence of transient ”Kasner epochs” — BKL oscillations. Later it was found that some classes of an anisotropic matter can induce similar type of cosmological behavior even in flat Bianchi I case. This can be shown for a magnetic field by LeBlanc and for a general vector field by Kirillov. At present, different modifications of General Relativity are widely used in cosmology. Therefore it is interesting to clear up does the oscillatory BKL-like regime exist in cosmological models with modified gravity. In this work we deal with Lovelock gravity; specifically, we consider Gauss-Bonnet term. Lovelock gravity gives corrections to GR only in higher-dimensional space-time; besides, cosmology with Gauss-Bonnet term in the (4+1)-dimensional case has some pathological features; so, in what follows we shall examine (N+1)-dimensional space-time with N>5.