Quadratic gravity potentials in de Sitter spacetime from Feynman diagrams

TL;DR

This paper calculates the Newtonian potential in quadratic gravity within de Sitter spacetime, revealing curvature-induced modifications at large distances and confirming the potential's vanishing beyond the Hubble radius, with implications for modified gravity theories.

Contribution

It provides a covariant computation of the scalar Green's function and classical potential in quadratic gravity on de Sitter background, including curvature effects and their relation to modified Newtonian dynamics.

Findings

Reproduces flat-spacetime Yukawa potential at short distances

Shows potential vanishes beyond the Hubble radius

Identifies curvature effects on the Newtonian potential

Abstract

We employ a manifestly covariant formalism to compute the tree-level amputated Green's function of non-minimally coupled scalar fields in quadratic gravity in a de Sitter background. We study this Green's function in the adiabatic limit, and construct the classical Newtonian potential. At short distances, the flat-spacetime Yukawa potential is reproduced, while the curvature gives rise to corrections to the potential at large distances. Beyond the Hubble radius, the potential vanishes identically, in agreement with the causal structure of de Sitter spacetime. For sub-Hubble distances, we investigate whether the modifications to the potential reproduce Modified Newtonian Dynamics.