Accelerating cosmologies in Lovelock gravity with dilaton

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.Comment: 23 page

Quadratic theory of gravity with a scalar field and type I Shapovalov wave spacetimes

For the quadratic theory of gravity with a scalar field, exact solutions are found for gravitational-wave models in Shapovalov I-type spacetimes, which do not arise in models of the general theory of relativity. The theory of gravity under consideration can effectively describe the early stages of the universe. Type I Shapovalov spaces are the most general forms of gravitational-wave Shapovalov spacetimes, whose metrics in privileged coordinate systems depend on three variables, including the wave variable. For Einstein vacuum spacetimes, these wave models degenerate into simpler types. The exact models of gravitational waves in the quadratic theory of gravity can be used to test the realism of such theories of gravity