Abstract
Many theories of modified gravity with higher order derivatives are usually ignored because of serious problems that appear due to an additional ghost degree of freedom. Most dangerously, it causes an immediate decay of the vacuum. However, breaking Lorentz invariance can cure such abominable behavior. By analyzing a model that describes a massive graviton together with a remaining Boulware-Deser ghost mode we show that even ghostly theories of modified gravity can yield models that are viable at both classical and quantum levels and, therefore, they should not generally be ruled out. Furthermore, we identify the most dangerous quantum scattering process that has the main impact on the decay time and find differences to simple theories that only describe an ordinary scalar field and a ghost. Additionally, constraints on the parameters of the theory including some upper bounds on the Lorentz-breaking cutoff scale are presented. In particular, for a simple theory of massive gravity we find that a breaking of Lorentz invariance is allowed to happen even at scales above the Planck mass. Finally, we discuss the relevance to other theories of modified gravity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Supernova Search Team collaboration, A.G. Riess et al., Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116 (1998) 1009 [astro-ph/9805201] [INSPIRE].
Supernova Cosmology Project collaboration, S. Perlmutter et al., Measurements of Omega and Lambda from 42 high redshift supernovae, Astrophys. J. 517 (1999) 565 [astro-ph/9812133] [INSPIRE].
P. Bull et al., Beyond ΛCDM: Problems, solutions and the road ahead, Phys. Dark Univ. 12 (2016) 56 [arXiv:1512.05356] [INSPIRE].
H. Vermeil, Notiz über das mittler Krümmungsmass einer n-fach ausgedehnten Riemannschen Mannigfaltigkeit, Nachr. Ges. Wiss. Göttingen (1917) 334.
É. Cartan, Sur les équations de la gravitation d’Einstein, J. Math. Pure Appl. 1 (1922) 141.
D. Lovelock, The four-dimensionality of space and the Einstein tensor, J. Math. Phys. 13 (1972) 874 [INSPIRE].
J. Navarro and J.B. Sancho, On the naturality of the Einstein equation, J. Geom. Phys. 58 (2008) 1007 [arXiv:0709.1928] [INSPIRE].
H. Motohashi and T. Suyama, Third order equations of motion and the Ostrogradsky instability, Phys. Rev. D 91 (2015) 085009 [arXiv:1411.3721] [INSPIRE].
M. Twain, A ghost story, San Francisco Chronicle (1875).
R.P. Woodard, Avoiding dark energy with 1/r modifications of gravity, Lect. Notes Phys. 720 (2007) 403 [astro-ph/0601672] [INSPIRE].
F. Sbisà, Classical and quantum ghosts, Eur. J. Phys. 36 (2015) 015009 [arXiv:1406.4550] [INSPIRE].
S.M. Carroll, M. Hoffman and M. Trodden, Can the dark energy equation-of-state parameter w be less than −1?, Phys. Rev. D 68 (2003) 023509 [astro-ph/0301273] [INSPIRE].
D.E. Kaplan and R. Sundrum, A symmetry for the cosmological constant, JHEP 07 (2006) 042 [hep-th/0505265] [INSPIRE].
S. Dyda, E.E. Flanagan and M. Kamionkowski, Vacuum Instability in Chern-Simons Gravity, Phys. Rev. D 86 (2012) 124031 [arXiv:1208.4871] [INSPIRE].
S. Ramazanov, F. Arroja, M. Celoria, S. Matarrese and L. Pilo, Living with ghosts in Hořava-Lifshitz gravity, JHEP 06 (2016) 020 [arXiv:1601.05405] [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.
S.F. Hassan and R.A. Rosen, Confirmation of the Secondary Constraint and Absence of Ghost in Massive Gravity and Bimetric Gravity, JHEP 04 (2012) 123 [arXiv:1111.2070] [INSPIRE].
P. Creminelli, A. Nicolis, M. Papucci and E. Trincherini, Ghosts in massive gravity, JHEP 09 (2005) 003 [hep-th/0505147] [INSPIRE].
C. de Rham and G. Gabadadze, Generalization of the Fierz-Pauli Action, Phys. Rev. D 82 (2010) 044020 [arXiv:1007.0443] [INSPIRE].
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].
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].
C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of Massive Gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE].
S.F. Hassan, A. Schmidt-May and M. von Strauss, Proof of Consistency of Nonlinear Massive Gravity in the Stúckelberg Formulation, Phys. Lett. B 715 (2012) 335 [arXiv:1203.5283] [INSPIRE].
D.G. Boulware and S. Deser, Can gravitation have a finite range?, Phys. Rev. D 6 (1972) 3368 [INSPIRE].
J.M. Cline, S. Jeon and G.D. Moore, The phantom menaced: Constraints on low-energy effective ghosts, Phys. Rev. D 70 (2004) 043543 [hep-ph/0311312] [INSPIRE].
S.F. Hassan and R.A. Rosen, On Non-Linear Actions for Massive Gravity, JHEP 07 (2011) 009 [arXiv:1103.6055] [INSPIRE].
M. Fasiello and A.J. Tolley, Cosmological perturbations in Massive Gravity and the Higuchi bound, JCAP 11 (2012) 035 [arXiv:1206.3852] [INSPIRE].
G. D’Amico, C. de Rham, S. Dubovsky, G. Gabadadze, D. Pirtskhalava and A.J. Tolley, Massive Cosmologies, Phys. Rev. D 84 (2011) 124046 [arXiv:1108.5231] [INSPIRE].
K. Hinterbichler, Theoretical Aspects of Massive Gravity, Rev. Mod. Phys. 84 (2012) 671 [arXiv:1105.3735] [INSPIRE].
C. de Rham, Massive Gravity, Living Rev. Rel. 17 (2014) 7.
N. Afshordi, Why is High Energy Physics Lorentz Invariant?, arXiv:1511.07879 [INSPIRE].
J.M. Martin-Garcia, xAct: Efficient tensor computer algebra for the Wolfram Language, http://www.xact.es.
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1605.08757
This work is dedicated to our friend, Tham.
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Könnig, F., Nersisyan, H., Akrami, Y. et al. A spectre is haunting the cosmos: quantum stability of massive gravity with ghosts. J. High Energ. Phys. 2016, 118 (2016). https://doi.org/10.1007/JHEP11(2016)118
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2016)118