On Consistent Kinetic and Derivative Interactions for Gravitons

TL;DR

This paper proposes new kinetic and derivative interactions for spin-2 fields that break diffeomorphism invariance, potentially enabling ghost-free massive gravity theories with healthy degrees of freedom.

Contribution

It introduces a new family of kinetic and derivative interactions for gravitons that extend beyond Einstein-Hilbert, exploring their consistency and implications for massive and multi-gravity theories.

Findings

New kinetic interactions can propagate 5 degrees of freedom for a single spin-2 field.

Conditions under which these interactions lead to healthy effective field theories.

Frameworks for 'Jordan' and 'Einstein' frames in multi-gravity contexts.

Abstract

The only known fully ghost-free and consistent Lorentz-invariant kinetic term for a graviton (or indeed for any spin-2 field) is the Einstein-Hilbert term. Here we propose and investigate a new family of candidate kinetic interactions and their extensions to derivative interactions involving several spin-2 fields. These new terms generically break diffeomorphism invariance(s) and as a result can lead to the propagation of 5 degrees of freedom for a single spin-2 field - analogous to ghost-free Massive Gravity. We discuss under what circumstances these new terms can be used to build healthy effective field theories and in the process establish the `Jordan' and `Einstein' frame pictures for Massive-, Bi- and Multi-Gravity.