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

TL;DR

This work proves that the de Rham-Gabadadze-Tolley (dRGT) massive gravity model propagates five degrees of freedom on generic backgrounds, thereby avoiding the Boulware-Deser ghost. By recasting FP as GR plus four scalar fields and aligning the field-space basis with the background, the authors show that the dangerous sixth mode does not arise in the dRGT class, and they extend the argument to general reference metrics. A key byproduct is a practical method to obtain dispersion relations for vector and scalar modes around arbitrary backgrounds, along with a dynamic assessment of the scalar mode’s cutoff scale in terms of background nonlinearities or curvature. The results imply that the theory remains ghost-free beyond Minkowski, though background-dependent pathologies (superluminal propagation or ghost-like behavior) can occur, motivating careful background-by-background analysis for phenomenology and consistency. The framework also clarifies the role of the decoupling limit and supports generalizations to different reference metrics in the broader ghost-free massive gravity program.

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.