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In de Rham-Gabadadze-Tolley (dRGT) massive gravity and bigravity, anon-minimal matter coupling involving both metrics generically re-introducesthe Boulware--Deser (BD) ghost. A non-minimal matter coupling via a simple, yetspecific composite metric has been proposed, which eliminates the BD ghostbelow the strong coupling scale. Working explicitly in the metric formulationand for arbitrary spacetime dimensions, we show that this composite metric isthe unique consistent non-minimal matter coupling below the strong couplingscale, which emerges out of two diagnostics, namely, absence of Ostrogradskighosts in the decoupling limit and absence of the BD ghost from matter quantumloop corrections.

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