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Title: Massive graviton on arbitrary background: derivation, syzygies, applications

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 reachmore » 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.« less
Authors:
 [1] ;  [1] ;  [2] ;  [1]
  1. UPMC-CNRS, UMR7095, Institut d’Astrophysique de Paris, GReCO,98bis boulevard Arago, F-75014 Paris (France)
  2. (France)
Publication Date:
OSTI Identifier:
22458436
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 06; Other Information: PUBLISHER-ID: JCAP06(2015)038; OAI: oai:repo.scoap3.org:10783; cc-by Article funded by SCOAP3. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Country of input: International Atomic Energy Agency (IAEA)
Sponsoring Org:
SCOAP3, CERN, Geneva (Switzerland)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; EQUATIONS OF MOTION; FIELD EQUATIONS; GRAVITATION; LIMITING VALUES; METRICS; NONLUMINOUS MATTER; SPACE-TIME