Manifestations of Horndeski theory in binary systems with pulsars

There are two problems in modern physics, which can not be explained by the generally recognized gravitational theory (general relativity). The first of them is dark matter (DM), it is invisible matter, which fills up in galaxies and manifests itself only in the gravitational interaction. The second problem is dark energy (DE), this phenomenon is responsible for accelerating the expansion of the Universe. One of the ways to solve these problems is to develop modified gravity. Adding the scalar field to general relativity is one of possible expansions of gravitational theory. The Horndeski theory is the most general scalar-tensor theory with second-order field equations. In this paper, the subclass of Horndeski gravity without Vainstein screening mechanism is tested in strong field regime of binary pulsars. Two specific cases of the Horndeski gravity are considered: the hybrid metric-Palatini f(R)-gravity and massive Brans-Dicke theory. The observational data of binary pulsars is used for obtaining constraints. (authors)