What do gravitons say about (unimodular) gravity?

TL;DR

This paper investigates the constraints on weak field gravity theories from S-matrix properties, showing that only General Relativity and Unimodular Gravity are consistent with unitarity and Lorentz invariance, and confirming their S-matrix equivalence.

Contribution

It demonstrates that only two weak field Lagrangians, corresponding to GR and Unimodular Gravity, satisfy S-matrix constraints, establishing their equivalence around flat spacetime.

Findings

Only GR and Unimodular Gravity yield consistent covariant interactions.

The S-matrix of both theories is equivalent around flat spacetime.

On-shell gauge invariance corresponds to transverse linearised diffeomorphisms.

Abstract

We revisit the problem of constraining the weak field limit of the gravitational lagrangian from S-matrix properties. From unitarity and Lorentz invariance of the S-matrix of massless gravitons, we derive on-shell gauge invariance to consist on the transverse part of the linearised diffeomorphisms group. Moreover, by looking to the interaction between sources, we conclude that there exist only two possible lagrangians that lead to a well-defined covariant interaction, corresponding to the weak field limits of General Relativity and Unimodular Gravity. Additionally, this result confirms the equivalence of the S-matrix of both theories around flat space-time.