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Ghost-free massive gravity with a general reference metric

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Abstract

Theories of massive gravity inevitably include an auxiliary reference metric. Generically, they also contain an inconsistency known as the Boulware-Deser ghost. Recently, a family of non-linear massive gravity actions, formulated with a flat reference metric, were proposed and shown to be ghost free at the complete non-linear level. In this paper we consider these non-linear massive gravity actions but now formulated with a general reference metric. We extend the proof of the absence of the Boulware-Deser ghost to this case. The analysis is carried out in the ADM formalism at the complete non-linear level. We show that in these models there always exists a Hamiltonian constraint which, with an associated secondary constraint, eliminates the ghost. This result considerably extends the range of known consistent non-linear massive gravity theories. In addition, these theories can also be used to describe a massive spin-2 field in an arbitrary, fixed gravitational background. We also discuss the positivity of the Hamiltonian.

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Authors and Affiliations

  1. Department of Physics & The Oskar Klein Centre, Stockholm University, AlbaNova University Centre, SE-106 91, Stockholm, Sweden

    S. F. Hassan & Angnis Schmidt-May

  2. Physics Department and Institute for Strings, Cosmology, and Astroparticle Physics, Columbia University, New York, NY, 10027, U.S.A

    Rachel A. Rosen

Authors
  1. S. F. Hassan
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  2. Rachel A. Rosen
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  3. Angnis Schmidt-May
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Correspondence to S. F. Hassan.

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ArXiv ePrint: 1109.3230

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Hassan, S.F., Rosen, R.A. & Schmidt-May, A. Ghost-free massive gravity with a general reference metric. J. High Energ. Phys. 2012, 26 (2012). https://doi.org/10.1007/JHEP02(2012)026

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