Anisotropic and inhomogeneous cosmological models in the scalar-tensor theory of gravity with non-minimal kinetic coupling

In this paper, we consider a gravitating scalar field with a non-minimal kinetic coupling to the curvature. The field equations are written in the polarized Gaud? metric. The corresponding space-time is anisotropic and inhomogeneous. In our research, we want to obtain mechanisms for the transition of the Universe from an inhomogeneous phase to a homogeneous one in the framework of Horndesky’s theory. In this paper, we restrict ourselves to a preliminary analysis of the field equations.