# Graviton spectrum in simplified Dark Matter models with graviton mediators in the de Sitter space

## TL;DR

This paper calculates the correction to the graviton spectrum in a cosmological background due to Dark Matter interactions, providing a model-independent result applicable to various Dark Matter scenarios in de Sitter space.

## Contribution

It presents a universal, second-order correction to the graviton two-point function in simplified Dark Matter models with graviton mediators in de Sitter space, independent of Dark Matter field specifics.

## Key findings

- Derived a model-independent correction to the graviton spectrum.
- Applied the framework to a massive scalar Dark Matter model.
- Calculated the first-order correction in the adiabatic regime.

## Abstract

This is the second in a series of papers investigating the formulation of the simplified Dark Matter models with graviton mediators in cosmological backgrounds. We address here the crucial problem of the fundamental observable of interest, namely the graviton spectrum in a FRW cosmological background with an arbitrary Dark Matter background component. We calculate the correction to the free graviton two-point function up to the second order in the coupling constant between the Dark Matter and the graviton in the simplified Dark Matter model with graviton mediators approach in the de Sitter space. Our result is model independent in the sense that it does not depend on the particular form of the Dark Matter fields. Also, due to the universality of the interaction between the Dark Matter and the graviton, the result obtained here apply to the interaction between the baryonic matter and the gravitons. As an application, we discuss in detail the massive scalar Dark Matter model and calculate the first order correction to the two-point function due to two Dark Matter modes in the adiabatic regime.