On the uniqueness of the non-minimal matter coupling in massive gravity and bigravity

TL;DR

This paper proves that a specific composite metric is the only consistent non-minimal matter coupling in massive gravity and bigravity theories that avoids the Boulware-Deser ghost below the strong coupling scale.

Contribution

It demonstrates the uniqueness of a particular composite metric as the sole consistent non-minimal matter coupling in these theories, based on ghost absence diagnostics.

Findings

The composite metric eliminates the BD ghost below the strong coupling scale.

It is the unique non-minimal matter coupling satisfying ghost-free conditions.

The proof applies in arbitrary spacetime dimensions.

Abstract

In de Rham-Gabadadze-Tolley (dRGT) massive gravity and bigravity, a non-minimal matter coupling involving both metrics generically re-introduces the Boulware--Deser (BD) ghost. A non-minimal matter coupling via a simple, yet specific composite metric has been proposed, which eliminates the BD ghost below the strong coupling scale. Working explicitly in the metric formulation and for arbitrary spacetime dimensions, we show that this composite metric is the unique consistent non-minimal matter coupling below the strong coupling scale, which emerges out of two diagnostics, namely, absence of Ostrogradski ghosts in the decoupling limit and absence of the BD ghost from matter quantum loop corrections.