Massive graviton on arbitrary background: derivation, syzygies, applications

Journal Article · Tue Jun 23 04:00:00 EDT 2015 · Journal of Cosmology and Astroparticle Physics

DOI:https://doi.org/10.1088/1475-7516/2015/06/038· OSTI ID:22458436

Bernard, Laura ^[1]; Deffayet, Cédric ^[1]; Strauss, Mikael von ^[1]

---

1. UPMC-CNRS, UMR7095, Institut d’Astrophysique de Paris, GReCO,98bis boulevard Arago, F-75014 Paris (France)

We give the detailed derivation of the fully covariant form of the quadratic action and the derived linear equations of motion for a massive graviton in an arbitrary background metric (which were presented in arXiv:1410.8302 [hep-th]). Our starting point is the de Rham-Gabadadze-Tolley (dRGT) family of ghost free massive gravities and using a simple model of this family, we are able to express this action and these equations of motion in terms of a single metric in which the graviton propagates, hence removing in particular the need for a “reference metric' which is present in the non perturbative formulation. 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. This last constraint involves powers and combinations of the curvature of the background metric. The 5 constraints are obtained for a background metric which is unconstrained, i.e. which does not have to obey the background field equations. We then apply these results to the case of Einstein space-times, where we show that the 5 constraints become trivial, and Friedmann-Lemaître-Robertson-Walker space-times, for which we correct in particular some results that appeared elsewhere. To reach our results, we derive several non trivial identities, syzygies, involving the graviton fields, its derivatives and the background metric curvature. These identities have their own interest. We also discover that there exist backgrounds for which the dRGT equations cannot be unambiguously linearized.

• Sponsoring Organization: SCOAP3, CERN, Geneva (Switzerland)
• OSTI ID: 22458436
• Journal Information: Journal of Cosmology and Astroparticle Physics, Journal Name: Journal of Cosmology and Astroparticle Physics Journal Issue: 06 Vol. 2015; ISSN 1475-7516
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
EQUATIONS OF MOTION
FIELD EQUATIONS
GRAVITATION
LIMITING VALUES
METRICS
NONLUMINOUS MATTER
SPACE-TIME