Abstract
In massive gravity and in bimetric theories of gravity, two constraints are needed to eliminate the two phase-space degrees of freedom of the Boulware-Deser ghost. For recently proposed non-linear theories, a Hamiltonian constraint has been shown to exist and an associated secondary constraint was argued to arise as well. In this paper we explicitly demonstrate the existence of the secondary constraint. Thus the Boulware-Deser ghost is completely absent from these non-linear massive gravity theories and from the corresponding bimetric theories. Equivalently, this proves the existence of classically ghost-free theories of massive spin-2 fields, in both fixed and dynamical gravitational backgrounds.
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References
D. Boulware and S. Deser, Can gravitation have a finite range?, Phys. Rev. D 6 (1972) 3368 [INSPIRE].
S. Hassan and R.A. Rosen, Resolving the ghost problem in non-linear massive gravity, Phys. Rev. Lett. 108 (2012) 041101 [arXiv:1106.3344] [INSPIRE].
S. 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].
S. Hassan and R.A. Rosen, Bimetric gravity from ghost-free massive gravity, JHEP 02 (2012) 126 [arXiv:1109.3515] [INSPIRE].
C. de Rham and G. Gabadadze, Generalization of the Fierz-Pauli action, Phys. Rev. D 82 (2010) 044020 [arXiv:1007.0443] [INSPIRE].
C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of massive gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE].
C. de Rham, G. Gabadadze and A. Tolley, Ghost free massive gravity in the Stückelberg language, Phys. Lett. B 711 (2012) 190 [arXiv:1107.3820] [INSPIRE].
C. de Rham, G. Gabadadze and A.J. Tolley, Helicity decomposition of ghost-free massive gravity, JHEP 11 (2011) 093 [arXiv:1108.4521] [INSPIRE].
C. Deffayet and S. Randjbar-Daemi, Non linear Fierz-Pauli theory from torsion and bigravity, Phys. Rev. D 84 (2011) 044053 [arXiv:1103.2671] [INSPIRE].
A.H. Chamseddine and V. Mukhanov, Massive gravity simplified: a quadratic action, JHEP 08 (2011) 091 [arXiv:1106.5868] [INSPIRE].
C. Deffayet and T. Jacobson, On horizon structure of bimetric spacetimes, Class. Quant. Grav. 29 (2012) 065009 [arXiv:1107.4978] [INSPIRE].
C. de Rham, G. Gabadadze and A.J. Tolley, Comments on (super)luminality, arXiv:1107.0710 [INSPIRE].
S. Folkerts, A. Pritzel and N. Wintergerst, On ghosts in theories of self-interacting massive spin-2 particles, arXiv:1107.3157 [INSPIRE].
G. D’Amico, C. de Rham, S. Dubovsky, G. Gabadadze, D. Pirtskhalava, et al., Massive cosmologies, Phys. Rev. D 84 (2011) 124046 [arXiv:1108.5231] [INSPIRE].
A.E. Gumrukcuoglu, C. Lin and S. Mukohyama, Open FRW universes and self-acceleration from nonlinear massive gravity, JCAP 11 (2011) 030 [arXiv:1109.3845] [INSPIRE].
K. Koyama, G. Niz and G. Tasinato, The self-accelerating universe with vectors in massive gravity, JHEP 12 (2011) 065 [arXiv:1110.2618] [INSPIRE].
L. Alberte, Massive gravity on curved background, arXiv:1110.3818 [INSPIRE].
J. Kluson, Hamiltonian analysis of 1 + 1 dimensional massive gravity, Phys. Rev. D 85 (2012) 044010 [arXiv:1110.6158] [INSPIRE].
K. Hinterbichler, Theoretical aspects of massive gravity, arXiv:1105.3735 [INSPIRE].
S. Hassan and R.A. Rosen, On non-linear actions for massive gravity, JHEP 07 (2011) 009 [arXiv:1103.6055] [INSPIRE].
D. Comelli, M. Crisostomi, F. Nesti and L. Pilo, Spherically symmetric solutions in ghost-free massive gravity, Phys. Rev. D 85 (2012) 024044 [arXiv:1110.4967] [INSPIRE].
M.S. Volkov, Cosmological solutions with massive gravitons in the bigravity theory, JHEP 01 (2012) 035 [arXiv:1110.6153] [INSPIRE].
M. von Strauss, A. Schmidt-May, J. Enander, E. Mortsell and S. Hassan, Cosmological solutions in bimetric gravity and their observational tests, JCAP 03 (2012) 042 [arXiv:1111.1655] [INSPIRE].
M. Fierz, Force-free particles with any spin, Helv. Phys. Acta 12 (1939) 3 [INSPIRE].
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].
J. Kluson, Note about hamiltonian structure of non-linear massive gravity, JHEP 01 (2012) 013 [arXiv:1109.3052] [INSPIRE].
R.L. Arnowitt, S. Deser and C.W. Misner, The dynamics of general relativity, gr-qc/0405109 [INSPIRE].
J. Khoury, G.E. Miller and A.J. Tolley, Spatially covariant theories of a transverse, traceless graviton, part I: formalism, Phys. Rev. D 85 (2012) 084002 [arXiv:1108.1397] [INSPIRE].
A. Higuchi, Forbidden mass range for spin-2 field theory in de Sitter space-time, Nucl. Phys. B 282 (1987) 397 [INSPIRE].
S. Deser and A. Waldron, Partial masslessness of higher spins in (A)dS, Nucl. Phys. B 607 (2001) 577 [hep-th/0103198] [INSPIRE].
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ArXiv ePrint: 1111.2070
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Hassan, S.F., Rosen, R.A. Confirmation of the secondary constraint and absence of ghost in massive gravity and bimetric gravity. J. High Energ. Phys. 2012, 123 (2012). https://doi.org/10.1007/JHEP04(2012)123
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DOI: https://doi.org/10.1007/JHEP04(2012)123