Gravity-mediated Dark Matter models in the de Sitter space

In this paper, we generalize the simplified Dark Matter models with graviton mediator to the curved space-time, in particular to the de Sitter space. We obtain the generating functional of the Green's functions in the Euclidean de Sitter space for the covariant free gravitons. We determine the generating functional of the interacting theory between Dark Matter particles and the covariant gravitons. Also, we calculate explicitly the 2-point and 3-point interacting Green's functions for the symmetric traceless divergence-less covariant graviton. The results derived here are general in the sense that they do not depend on a particular model for the Dark Matter component and they show that the quantum effects of the interaction between the Dark Matter and the gravitons in the de Sitter space are computable by the methods of the standard Quantum Field Theory techniques.