Consistent massive graviton on arbitrary backgrounds

TL;DR

This paper derives covariant linearized equations for massive gravitons in arbitrary backgrounds within dRGT gravity, eliminating auxiliary metrics and ensuring ghost-free constraints.

Contribution

It provides a fully covariant linearized framework for massive gravitons on arbitrary backgrounds, including constraints that remove ghost degrees of freedom.

Findings

Derived covariant linearized field equations for massive gravitons.

Eliminated non-dynamical metrics in certain dRGT theories.

Established five covariant constraints ensuring ghost freedom.

Abstract

We obtain the fully covariant linearized field equations for the metric perturbation in the de Rham-Gabadadze-Tolley (dRGT) ghost free massive gravities. For a subset of these theories, we show that the non dynamical metric that appears in the dRGT setup can be completely eliminated leading to the theory of a massive graviton moving in a single metric. This has a mass term which contains non trivial contributions of the space-time curvature. We show further how 5 covariant constraints can be obtained including one which leads to the tracelessness of the graviton on flat space-time and removes the Boulware-Deser ghost. The 5 constraints are obtained for a background metric which is arbitrary, i.e. which does not have to obey the background field equations.