Cosmological solutions in the Lovelock theory and the Einstein-Gauss-Bonnet theory with a dilaton

For a description of the expanding Universe agreeing with the observational data, one of the models of modified gravity is chosen, the Lovelock theory with a dilaton. We have considered an empty D-dimensional space-time with two maximally symmetric subspaces, one being 3-dimensional, the other (D-4)-dimensional. In different versions of the theory under study (in the third order without a dilaton an in the second order, i.e., in the Einstein-Gauss-Bonnet theory with a dilaton), a number of exact and approximate cosmological solutions have been obtained. Among them we have selected the solutions describing an accelerated expansion of the 3-dimensional space. The unobservability of the extra space is explained with the aid of the Kaluza-Klein approach.