Advertisement

Journal of High Energy Physics

, 2012:126 | Cite as

Bimetric gravity from ghost-free massive gravity

  • S. F. Hassan
  • Rachel A. Rosen
Article

Abstract

Generically, non-linear bimetric theories of gravity suffer from the same Boulware-Deser ghost instability as non-linear theories of massive gravity. However, recently proposed theories of massive gravity have been shown to be ghost-free. These theories are formulated with respect to a flat, non-dynamical reference metric. In this work we show that it is possible to give dynamics to the reference metric in such a way that the consistency of the theory is maintained. The result is a non-linear bimetric theory of a massless spin-2 field interacting with a massive spin-2 field that is free of the Boulware-Deser ghost. To our knowledge, this is the first construction of such a ghost-free bimetric theory.

Keywords

Classical Theories of Gravity Space-Time Symmetries 

References

  1. [1]
    C.J. Isham, A. Salam and J.A. Strathdee, F-dominance of gravity, Phys. Rev. D 3 (1971) 867 [INSPIRE].MathSciNetADSGoogle Scholar
  2. [2]
    D.G. Boulware and S. Deser, Can gravitation have a finite range?, Phys. Rev. D 6 (1972) 3368 [INSPIRE].ADSGoogle Scholar
  3. [3]
    M. Fierz, Force-free particles with any spin, Helv. Phys. Acta 12 (1939) 3 [INSPIRE].CrossRefGoogle Scholar
  4. [4]
    M. Fierz and W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Roy. Soc. Lond. A 173 (1939) 211 [INSPIRE].MathSciNetADSGoogle Scholar
  5. [5]
    C. de Rham and G. Gabadadze, Generalization of the Fierz-Pauli action, Phys. Rev. D 82 (2010) 044020 [arXiv:1007.0443] [INSPIRE].ADSGoogle Scholar
  6. [6]
    C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of massive gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    S.F. Hassan and R.A. Rosen, Resolving the ghost problem in non-linear massive gravity, Phys. Rev. Lett. 108 (2012) 041101 [arXiv:1106.3344] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    S.F. Hassan and R.A. Rosen, On non-linear actions for massive gravity, JHEP 07 (2011) 009 [arXiv:1103.6055] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    C. de Rham, G. Gabadadze and A.J. Tolley, Ghost free massive gravity in the Stückelberg language, arXiv:1107.3820 [INSPIRE].
  10. [10]
    C. de Rham, G. Gabadadze and A.J. Tolley, Helicity decomposition of ghost-free massive gravity, JHEP 11 (2011) 093 [arXiv:1108.4521] [INSPIRE].CrossRefGoogle Scholar
  11. [11]
    K. Hinterbichler, Theoretical aspects of massive gravity, arXiv:1105.3735 [INSPIRE].
  12. [12]
    T. Damour, I.I. Kogan and A. Papazoglou, Nonlinear bigravity and cosmic acceleration, Phys. Rev. D 66 (2002) 104025 [hep-th/0206044] [INSPIRE].MathSciNetADSGoogle Scholar
  13. [13]
    C. Aragone and S. Deser, Constraints on gravitationally coupled tensor fields, Nuovo Cim. A 3 (1971) 709 [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    C. Aragone and S. Deser, Consistency problems of spin-2 gravity coupling, Nuovo Cim. B 57 (1980) 33 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    A. Salam and J.A. Strathdee, A class of solutions for the strong gravity equations, Phys. Rev. D 16 (1977) 2668 [INSPIRE].ADSGoogle Scholar
  16. [16]
    T. Damour and I.I. Kogan, Effective Lagrangians and universality classes of nonlinear bigravity, Phys. Rev. D 66 (2002) 104024 [hep-th/0206042] [INSPIRE].MathSciNetADSGoogle Scholar
  17. [17]
    N. Boulanger, T. Damour, L. Gualtieri and M. Henneaux, Inconsistency of interacting, multigraviton theories, Nucl. Phys. B 597 (2001) 127 [hep-th/0007220] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    S.F. Hassan, R.A. Rosen and A. Schmidt-May, Ghost-free massive gravity with a general reference metric, JHEP 02 (2012) 026 [arXiv:1109.3230] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    S.F. Hassan and R.A. Rosen, Confirmation of the secondary constraint and absence of ghost in massive gravity and bimetric gravity, arXiv:1111.2070 [INSPIRE].
  20. [20]
    R.L. Arnowitt, S. Deser and C.W. Misner, The dynamics of general relativity, gr-qc/0405109 [INSPIRE].

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.Department of Physics & The Oskar Klein Centre, Stockholm UniversityAlbaNova University CentreStockholmSweden
  2. 2.Physics Department and Institute for Strings, Cosmology, and Astroparticle PhysicsColumbia UniversityNew YorkU.S.A.

Personalised recommendations