A Note on Ghost-Free Matter Couplings in Massive Gravity and Multi-Gravity

TL;DR

This paper examines a non-minimal matter coupling in massive gravity and multi-gravity, demonstrating that it maintains the necessary constraints to eliminate the Boulware-Deser ghost beyond the decoupling limit when using unconstrained vielbeins.

Contribution

It shows that the proposed matter coupling preserves primary constraints to remove the ghost in a broad regime, extending previous results.

Findings

The matter coupling is ghost-free when formulated with unconstrained vielbeins.

Primary constraints are maintained beyond the decoupling limit.

The approach applies to both massive gravity and multi-gravity theories.

Abstract

We consider a recently proposed non-minimal matter coupling in massive gravity and multi-gravity. We argue that, when formulated in terms of unconstrained vielbeins, this matter coupling contains the primary constraints necessary to remove the Boulware-Deser ghost to all orders away from the decoupling limit.