Consistent massive graviton on arbitrary backgrounds

Laura Bernard (1) , Cédric Deffayet (1) , Mikael von Strauss (1)

1 IAP - Institut d'Astrophysique de Paris

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 nondynamical 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 nontrivial contributions of the space-time curvature. We show further how five 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 five constraints are obtained for a background metric which is arbitrary, i.e. which does not have to obey the background field equations.

Keywords: 04.50.Kd; Modified theories of gravity; High Energy Physics - Theory; General Relativity and Quantum Cosmology

Domains: Sciences of the Universe [physics]

Laura Bernard, Cédric Deffayet, Mikael von Strauss. Consistent massive graviton on arbitrary backgrounds. Physical Review D, 2015, 91, ⟨10.1103/PhysRevD.91.104013⟩. ⟨insu-03644944⟩