  For the description of the Universe expansion, compatible with observational
data, a model of modified gravity - Lovelock gravity with dilaton - is
investigated. D-dimensional space with 3- and (D-4)-dimensional maximally
symmetric subspaces is considered. Space without matter and space with perfect
fluid are under test. In various forms of the theory under way (third order
without dilaton and second order - Einstein-Gauss-Bonnet gravity - with dilaton
and without it) stationary, power-law, exponential and exponent-of-exponent
form cosmological solutions are obtained. Last two forms include solutions
which are clear to describe accelerating expansion of 3-dimensional subspace.
Also there is a set of solutions describing cosmological expansion which does
not tend to isotropization in the presence of matter.
