De Sitter scattering amplitudes in the Born approximation

TL;DR

This paper develops a covariant method to compute scattering amplitudes in de Sitter space, revealing how curvature influences gravitational interactions and potential behavior at different cosmological scales.

Contribution

It introduces a new covariant framework for calculating scattering amplitudes in de Sitter space, highlighting the effects of curvature on gravitational potentials.

Findings

Short-distance potential matches Newtonian gravity.

At Hubble-scale distances, the potential becomes repulsive due to curvature.

Beyond the horizon, the potential vanishes.

Abstract

We present a covariant framework to compute scattering amplitudes and potentials in a de Sitter background. In this setting, we compute the potential of a graviton-mediated scattering process involving two very massive scalars at tree level. Although the obtained scattering potential reproduces the Newtonian potential at short distances, on Hubble-size length scales it is affected by the constant curvature: effectively, it yields a repulsive force at sub-Hubble distances. This can be attributed to the expansion of the de Sitter universe. Beyond the de Sitter horizon, the potential vanishes identically. Hence, the scattering amplitude unveils the geometric properties of de Sitter spacetime in a novel and nontrivial way.