# Integral representation of the scalar propagators on the de Sitter expanding universe

## TL;DR

This paper introduces a novel integral representation for scalar propagators in de Sitter space, enabling the calculation of Feynman diagrams involving scalar particles in an expanding universe.

## Contribution

It presents a new integral representation that incorporates Heaviside functions, facilitating Feynman diagram calculations in de Sitter spacetime.

## Key findings

- Allows calculation of Feynman diagrams with scalar particles in de Sitter space
- Demonstrates the method with a second-order perturbation example
- Provides a practical tool for quantum field theory in curved spacetime

## Abstract

A new type of integral representation is proposed for the propagators of the massive Klein-Gordon field minimally coupled to the gravity of the de Sitter expanding universe. This representation encapsulates the effects of the Heaviside step functions of the Feynman propagators making possible for the first time the calculation of Feynman diagrams involving scalar particles on this background. In order to convince that, a simple example is given outlining the amplitudes in the second order of perturbations of the Compton effect in the de Sitter scalar quantum electrodynamics.