Cosmological perturbations in the theory of gravity with non-minimal kinetic coupling

In this paper, we consider cosmological perturbations in a theory with non-minimal kinetic coupling. We derive a set of equations for scalar, vector and tensor modes. The vector modes are analyzed for arbitrary curvature. The tensor modes and the scalar modes are analyzed for the open Universe model (K=0). It is shown that their behavior in quasi - de Sitter differs cardinally from the analogous behavior of modes in classical cosmology.