Built on

T. Regge and J.A. Wheeler, Stability of a Schwarzschild singularity, Phys. Rev. 108
1957
Earlier work this paper cites.
K.S. Stelle, Renormalization of higher-derivative quantum gravity, Phys. Rev. D 16
1977
Earlier work this paper cites.
K.S. Stelle, Classical gravity with higher derivatives, Gen. Rel. Grav. 9
1978
Earlier work this paper cites.
N.V. Krasnikov, Nonlocal gauge theories, Theor. Math. Phys. 73
1987
Earlier work this paper cites.
Yu.V. Kuz’min, The convergent nonlocal gravitation, Yad. Fiz. 50 (1989) 1630 [Sov. J. Nucl. Phys. 50 (1989) 1011]
1989
Earlier work this paper cites.
D. Christodoulou and S. Klainerman, The nonlinear stability of the Minkowski metric in general relativity, in Nonlinear Hyperbolic Problems , ed. by C. Carasso, P. Charrier, B. Hanouzet, and J.-L. Joly (Springer-Verlag, Berlin, 1989)
1989
Earlier work this paper cites.
V.A. Kostelecký and S. Samuel, Collective physics in the closed bosonic string, Phys. Rev. D 42
1990
Earlier work this paper cites.
D. Christodoulou, The stability of Minkowski spacetime, in Proceedings of the International Congress of Mathematicians, Kyoto 1990 , ed. by I. Satake (Springer-Verlag, Berlin, 1991)
1991
Earlier work this paper cites.
V.F. Mukhanov, H.A. Feldman, and R.H. Brandenberger, Theory of cosmological perturbations, Phys. Rept. 215
1992
Earlier work this paper cites.
A.A. Tseytlin, On singularities of spherically symmetric backgrounds in string theory, Phys. Lett. B 363
1995
Earlier work this paper cites.
A.G. Mirzabekian and G.A. Vilkovisky, The one loop form-factors in the effective action, and production of coherent gravitons from the vacuum, Classical Quantum Gravity 12
1995
Earlier work this paper cites.
M. Asorey, J.L. López, and I.L. Shapiro, Some remarks on high derivative quantum gravity, Int. J. Mod. Phys. A 12
1997
Earlier work this paper cites.
N. Dalal, D.E. Holz, S.A. Hughes, and B. Jain, Short GRB and binary black hole standard sirens as a probe of dark energy, Phys. Rev. D 74
2006
Earlier work this paper cites.
T. Biswas, A. Mazumdar, and W. Siegel, Bouncing universes in string-inspired gravity, J. Cosmol. Astropart. Phys. 0603 (2006) 009 [ arXiv:hep-th/0508194 ]
2006
Earlier work this paper cites.
J. Khoury, Fading gravity and self-inflation, Phys. Rev. D 76
2007
Earlier work this paper cites.
M. Maggiore, Gravitational Waves, Vols. 1 and 2 (Oxford University Press, Oxford, UK, 2007)
2007
Earlier work this paper cites.
H. Lindblad and I. Rodnianski, The global stability of Minkowski space-time in harmonic gauge, Ann. Math. 171
2010
Earlier work this paper cites.
S. Nissanke, D.E. Holz, S.A. Hughes, N. Dalal, and J.L. Sievers, Exploring short gamma-ray bursts as gravitational-wave standard sirens, Astrophys. J. 725
Original
2010
Earlier work this paper cites.
T. Biswas, T. Koivisto, and A. Mazumdar, Towards a resolution of the cosmological singularity in non-local higher derivative theories of gravity, JCAP 1011 (2010) 008 [ arXiv:1005.0590 ]
Original
2010
Earlier work this paper cites.

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2019

Nonlinear stability in nonlocal gravity

Briscese, Fabio, Calcagni, Gianluca, Modesto, Leonardo

Understand

We address the stability issue of Ricci-flat and maximally symmetric spacetimes in nonlocal gravity to all perturbative orders in the gravitational perturbation.

Assuming a potential at least cubic in curvature tensors but quadratic in the Ricci tensor, our proof consists on a mapping of the stability analysis in nonlocal gravity to the same problem in Einstein-Hilbert theory.
One of the consequences is that only the graviton field can propagate and the theory is ghost-free at all perturbative orders.
All the results known in Einstein gravity in vacuum with or without a cosmological constant can be exported to the case of nonlocal gravity: if a spacetime is stable at all perturbative orders in Einstein gravity, it is stable also in nonlocal gravity.

Built on

T. Regge and J.A. Wheeler, Stability of a Schwarzschild singularity, Phys. Rev. 108
1957
Earlier work this paper cites.
K.S. Stelle, Renormalization of higher-derivative quantum gravity, Phys. Rev. D 16
1977
Earlier work this paper cites.
K.S. Stelle, Classical gravity with higher derivatives, Gen. Rel. Grav. 9
1978
Earlier work this paper cites.
N.V. Krasnikov, Nonlocal gauge theories, Theor. Math. Phys. 73
1987
Earlier work this paper cites.
Yu.V. Kuz’min, The convergent nonlocal gravitation, Yad. Fiz. 50 (1989) 1630 [Sov. J. Nucl. Phys. 50 (1989) 1011]
1989
Earlier work this paper cites.
D. Christodoulou and S. Klainerman, The nonlinear stability of the Minkowski metric in general relativity, in Nonlinear Hyperbolic Problems , ed. by C. Carasso, P. Charrier, B. Hanouzet, and J.-L. Joly (Springer-Verlag, Berlin, 1989)
1989
Earlier work this paper cites.
V.A. Kostelecký and S. Samuel, Collective physics in the closed bosonic string, Phys. Rev. D 42
1990
Earlier work this paper cites.
D. Christodoulou, The stability of Minkowski spacetime, in Proceedings of the International Congress of Mathematicians, Kyoto 1990 , ed. by I. Satake (Springer-Verlag, Berlin, 1991)
1991
Earlier work this paper cites.
V.F. Mukhanov, H.A. Feldman, and R.H. Brandenberger, Theory of cosmological perturbations, Phys. Rept. 215
1992
Earlier work this paper cites.
A.A. Tseytlin, On singularities of spherically symmetric backgrounds in string theory, Phys. Lett. B 363
1995
Earlier work this paper cites.
A.G. Mirzabekian and G.A. Vilkovisky, The one loop form-factors in the effective action, and production of coherent gravitons from the vacuum, Classical Quantum Gravity 12
1995
Earlier work this paper cites.
M. Asorey, J.L. López, and I.L. Shapiro, Some remarks on high derivative quantum gravity, Int. J. Mod. Phys. A 12
1997
Earlier work this paper cites.
N. Dalal, D.E. Holz, S.A. Hughes, and B. Jain, Short GRB and binary black hole standard sirens as a probe of dark energy, Phys. Rev. D 74
2006
Earlier work this paper cites.
T. Biswas, A. Mazumdar, and W. Siegel, Bouncing universes in string-inspired gravity, J. Cosmol. Astropart. Phys. 0603 (2006) 009 [ arXiv:hep-th/0508194 ]
2006
Earlier work this paper cites.
J. Khoury, Fading gravity and self-inflation, Phys. Rev. D 76
2007
Earlier work this paper cites.
M. Maggiore, Gravitational Waves, Vols. 1 and 2 (Oxford University Press, Oxford, UK, 2007)
2007
Earlier work this paper cites.
H. Lindblad and I. Rodnianski, The global stability of Minkowski space-time in harmonic gauge, Ann. Math. 171
2010
Earlier work this paper cites.
S. Nissanke, D.E. Holz, S.A. Hughes, N. Dalal, and J.L. Sievers, Exploring short gamma-ray bursts as gravitational-wave standard sirens, Astrophys. J. 725
Original
2010
Earlier work this paper cites.
T. Biswas, T. Koivisto, and A. Mazumdar, Towards a resolution of the cosmological singularity in non-local higher derivative theories of gravity, JCAP 1011 (2010) 008 [ arXiv:1005.0590 ]
Original
2010
Earlier work this paper cites.