  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.
