Consistent massive graviton on arbitrary backgrounds

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.

Latex, 5 pages. Matches published version

References in corpus (4)

• Resummation of Massive Gravity
• Interacting Spin-2 Fields
• xPerm: fast index canonicalization for tensor computer algebra
• Covariant constraints in ghost free massive gravity

Cited by in corpus (11)

• Heavy spin-2 Dark Matter
• New Branches of Massive Gravity
• The dimensional reduction of linearized spin-2 theories invariant under transverse diffeomorphisms
• Massive gravitons in arbitrary spacetimes
• Massive spin-2 particles in a curved background via a nonsymmetric tensor
• Massive graviton on arbitrary background: derivation, syzygies, applications
• Note on massless and partially massless spin-2 particles in a curved background via a nonsymmetric tensor
• General Backgrounds for higher spin massive particles
• Generation of effective massive Spin-2 fields through spontaneous symmetry breaking of scalar field
• A link between ghost-free bimetric and Eddington-inspired Born-Infeld theory
• Multi-messenger lensing time delay as a probe of the graviton mass