Scattering amplitudes in super-renormalizable gravity

TL;DR

This paper calculates four-graviton scattering amplitudes in various super-renormalizable and finite gravity theories, finding they match Einstein gravity's amplitudes in most cases, with exceptions when Riemann tensor operators are added.

Contribution

It demonstrates that super-renormalizable and finite gravity theories have scattering amplitudes identical to Einstein gravity, except when Riemann tensor operators are included, which alter the results.

Findings

Amplitudes match Einstein gravity in most super-renormalizable theories.

Adding Riemann tensor operators changes the scattering amplitudes.

Four-graviton amplitudes in Weyl conformal gravity are zero.

Abstract

We explicitly compute the tree-level on-shell four-graviton amplitudes in four, five and six dimensions for local and weakly nonlocal gravitational theories that are quadratic in both, the Ricci and scalar curvature with form factors of the d'Alembertian operator inserted between. More specifically we are interested in renormalizable, super-renormalizable or finite theories. The scattering amplitudes for these theories turn out to be the same as the ones of Einstein gravity regardless of the explicit form of the form factors. As a special case the four-graviton scattering amplitudes in Weyl conformal gravity are identically zero. Using a field redefinition, we prove that the outcome is correct for any number of external gravitons (on-shell $n-$point functions) and in any dimension for a large class of theories. However, when an operator quadratic in the Riemann tensor is added in any dimension (with the exception of the Gauss-Bonnet term in four dimensions) the result is completely altered, and the scattering amplitudes depend on all the form factors introduced in the action.