A Proof Of Ghost Freedom In de Rham-Gabadadze-Tolley Massive Gravity

TL;DR

This paper proves that the de Rham-Gabadadze-Tolley massive gravity theory consistently propagates five degrees of freedom, confirming its ghost-free nature and providing insights into its symmetries and dispersion relations.

Contribution

It demonstrates the ghost freedom of the dRGT massive gravity theory around generic backgrounds and introduces an algorithm for dispersion relation analysis.

Findings

dRGT theory propagates five degrees of freedom

Decoupling limit ensures ghost freedom

Enhanced symmetry around linearized backgrounds

Abstract

We identify different helicity degrees of freedom of Fierz-Paulian massive gravity around generic backgrounds. We show that the two-parameter family proposed by de Rham, Gabadadze, and Tolley always propagates five degrees of freedom and therefore is free from the Boulware-Deser ghost. The analysis has a number of byproducts, among which (a) it shows how the original decoupling limit construction ensures ghost freedom of the full theory, (b) it reveals an enhanced symmetry of the theory around linearized backgrounds, and (c) it allows us to give an algorithm for finding dispersion relations. The proof naturally extends to generalizations of the theory with a reference metric different from Minkowski.