Abstract
This short note is devoted to the canonical analysis of the non-local theories of gravity. We find their Hamiltonian and determine the algebra of constraints. We perform this analysis for non-local theories of gravity formulated both in Jordan and Einstein frame. The result of our analysis is that Hamiltonian formulation does not bring to clear identification of ghosts presence in non-local gravity.
Similar content being viewed by others
References
Supernova Cosmology Project collaboration, S. Perlmutter et al., Measurements of Ω and Λ from 42 high-redshift supernovae, Astrophys. J. 517 (1999) 565 [astro-ph/9812133] [SPIRES].
WMAP collaboration, E. Komatsu et al., Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: cosmological interpretation, Astrophys. J. Suppl. 192 (2011) 18 [arXiv:1001.4538] [SPIRES].
S. Weinberg, The cosmological constant problem, Rev. Mod. Phys. 61 (1989) 1 [SPIRES].
M. Li, X.-D. Li, S. Wang and Y. Wang, Dark energy, arXiv:1103.5870 [SPIRES].
S. Nojiri and S.D. Odintsov, Introduction to modified gravity and gravitational alternative for dark energy, ECONF C 0602061 (2006) 06 [hep-th/0601213] [Int. J. Geom. Meth. Mod. Phys. 4 (2007) 115].
S. Nojiri and S.D. Odintsov, Unified cosmic history in modified gravity: from f(R) theory to Lorentz non-invariant models, Phys. Rept. 505 (2011) 59 [arXiv:1011.0544] [SPIRES].
A. De Felice and S. Tsujikawa, f(R) theories, Living Rev. Rel. 13 (2010) 3 [arXiv:1002.4928] [SPIRES].
S. Deser and R.P. Woodard, Nonlocal cosmology, Phys. Rev. Lett. 99 (2007) 111301 [arXiv:0706.2151] [SPIRES].
I.Y. Aref’eva, Nonlocal string tachyon as a model for cosmological dark energy, AIP Conf. Proc. 826 (2006) 301 [astro-ph/0410443] [SPIRES].
I.Y. Aref’eva, L.V. Joukovskaya and S.Y. Vernov, Dynamics in nonlocal linear models in the Friedmann-Robertson-Walker metric, J. Phys. A 41 (2008) 304003 [arXiv:0711.1364] [SPIRES].
L. Joukovskaya, Dynamics in nonlocal cosmological models derived from string field theory, Phys. Rev. D 76 (2007) 105007 [arXiv:0707.1545] [SPIRES].
G. Calcagni, M. Montobbio and G. Nardelli, Localization of nonlocal theories, Phys. Lett. B 662 (2008) 285 [arXiv:0712.2237] [SPIRES].
I.Y. Aref’eva and I.V. Volovich, Cosmological daemon, arXiv:1103.0273 [SPIRES].
F. Galli and A.S. Koshelev, Perturbative stability of SFT-based cosmological models, JCAP 05 (2011) 012 [arXiv:1011.5672] [SPIRES].
T. Biswas, J.A.R. Cembranos and J.I. Kapusta, Thermodynamics and cosmological constant of non-local field theories from p-adic strings, JHEP 10 (2010) 048 [arXiv:1005.0430] [SPIRES].
S. Capozziello, E. Elizalde, S. Nojiri and S.D. Odintsov, Accelerating cosmologies from non-local higher-derivative gravity, Phys. Lett. B 671 (2009) 193 [arXiv:0809.1535] [SPIRES].
G. Cognola, E. Elizalde, S. Nojiri, S.D. Odintsov and S. Zerbini, One-loop effective action for non-local modified Gauss-Bonnet gravity in de Sitter space, Eur. Phys. J. C 64 (2009) 483 [arXiv:0905.0543] [SPIRES].
S. Nojiri and S.D. Odintsov, Modified non-local-f(R) gravity as the key for the inflation and dark energy, Phys. Lett. B 659 (2008) 821 [arXiv:0708.0924] [SPIRES].
S. Jhingan et al., Phantom and non-phantom dark energy: the cosmological relevance of non-locally corrected gravity, Phys. Lett. B 663 (2008) 424 [arXiv:0803.2613] [SPIRES].
N. Arkani-Hamed, S. Dimopoulos, G. Dvali and G. Gabadadze, Non-local modification of gravity and the cosmological constant problem, hep-th/0209227 [SPIRES].
S. Nojiri, S.D. Odintsov, M. Sasaki and Y.-l. Zhang, Screening of cosmological constant in non-local gravity, Phys. Lett. B 696 (2011) 278 [arXiv:1010.5375] [SPIRES].
K. Bamba, S. Nojiri, S.D. Odintsov and M. Sasaki, Screening of cosmological constant for de Sitter universe in non-local gravity, phantom-divide crossing and finite-time future singularities, arXiv:1104.2692 [SPIRES].
M. Henneaux and C. Teitelboim, Quantization of gauge systems, Princeton University Press, Princeton U.S.A. (1992).
C.J. Isham and K.V. Kuchar, Representations of space-time diffeomorphisms. 1. Canonical parametrized field theories, Ann. Phys. 164 (1985) 288 [SPIRES].
C.J. Isham and K.V. Kuchar, Representations of space-time diffeomorphisms. 2. Canonical geometrodynamics, Ann. Phys. 164 (1985) 316 [SPIRES].
J.W. Moffat, Ultraviolet complete quantum gravity, Eur. Phys. J. Plus 126 (2011) 43 [arXiv:1008.2482] [SPIRES].
S.A. Hojman, K. Kuchar and C. Teitelboim, Geometrodynamics regained, Ann. Phys. 96 (1976) 88 [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1105.6056
Rights and permissions
About this article
Cite this article
Klusoň, J. Non-local gravity from hamiltonian point of view. J. High Energ. Phys. 2011, 1 (2011). https://doi.org/10.1007/JHEP09(2011)001
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2011)001