Аннотация:As known the Gauss-Bonnet term can be added to the four-dimensional Hilbert–Einstein action, but it does not change equations of gravity, because the Gauss-Bonnet term is a full derivative. The situation changes if one adds the term f(φ)G to the action, where f(φ)is a differentiable function of the scalar field φ. It is interesting that different types of modified gravity models with the Gauss-Bonnet term, including non-local models, can be presented as a gravitational model with non-minimally coupled scalar fields that include the term f(φ)G.
There are two basic motivations to modify gravity. The first one is an attempt to connect gravity with quantum physics by including quantum correction terms to Einstein’s
equations. In string theory inspired models the Gauss-Bonnet term arises naturally. The
second motivation is to describe the Universe evolution in a more natural way, without
the dark energy and/or the dark matter components. Gauss-Bonnet gravity models are
actively used to investigate either the dark energy domination era, the matter dominated
era and the inflation. So, the investigation of modified gravity models with the Gauss-Bonnet term is well motivated. In my report, I give a short review of cosmological models
with the Gauss-Bonnet term, including non-local ones.