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arXiv · 1401.3873

Covariant Approach to the No-ghost Theorem in Massive Gravity

Taichiro Kugo·Nobuyoshi Ohta
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Abstract

We discuss the no-ghost theorem in the massive gravity in a covariant manner. Using the BRST formalism and St\"{u}ckelberg 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 St\"{u}ckelberg `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 St\"{u}ckelberg scalar field, but show that this does not introduce the ghost into the theory.

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Taichiro Kugo, Nobuyoshi Ohta. 2014-01-16. Covariant Approach to the No-ghost Theorem in Massive Gravity. https://doi.org/10.1093/ptep/ptu046

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