Gravity-mediated Dark Matter models in the de Sitter space

TL;DR

This paper extends gravity-mediated Dark Matter models to de Sitter space, deriving Green's functions for covariant gravitons and Dark Matter interactions, demonstrating the computability of quantum effects in curved spacetime.

Contribution

It generalizes simplified Dark Matter models with graviton mediators to curved spacetime, providing explicit Green's functions in de Sitter space.

Findings

Derived the generating functional for free covariant gravitons in Euclidean de Sitter space.

Calculated explicit 2-point and 3-point Green's functions for covariant gravitons.

Showed quantum effects of Dark Matter-graviton interactions are computable using standard QFT methods.

Abstract

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.