Covariant Approach to the No-ghost Theorem in Massive Gravity

We discuss the no-ghost theorem in the massive gravity in a covariant manner. Using the BRST formalism and Stückelberg fields, we first clarify how the Boulware-Deser ghost decouples in the massive gravity theory with Fierz-Pauli mass term. Here we find that the crucial point in the proof is that there is no higher (time) derivative for the Stückelberg `scalar' field. We then analyze the nonlinear massive gravity proposed by de Rham, Gabadadze and Tolley, and show that there is no ghost for general admissible backgrounds. In this process, we find a very nontrivial decoupling limit for general backgrounds. We end the paper by demonstrating the general results explicitly in a nontrivial example where there apparently appear higher time derivatives for Stückelberg scalar field, but show that this does not introduce the ghost into the theory.

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