Nonlocal gravity. Conceptual aspects and cosmological predictions
Open accessAbstract
Even if the fundamental action of gravity is local, the corresponding quantum effective action, that includes the effect of quantum fluctuations, is a nonlocal object. These nonlocalities are well understood in the ultraviolet regime but much less in the infrared, where they could in principle give rise to important cosmological effects. Here we systematize and extend previous work of our group, in which it is assumed that a mass scale Λ is dynamically generated in the infrared, giving rise to nonlocal terms in the quantum effective action of gravity. We give a detailed discussion of conceptual aspects related to nonlocal gravity (including causality, degrees of freedom, ambiguities related to the boundary conditions of the nonlocal operator, scenarios for the emergence of a dynamical scale in the infrared) and of the cosmological consequences of these models. The requirement of providing a viable cosmological evolution severely restricts the form of the nonlocal terms, and selects a model (the so-called RR model) that corresponds to a dynamical mass generation for the conformal mode. For such a model: (1) there is a FRW background evolution, where the nonlocal term acts as an effective dark energy with a phantom equation of state, providing accelerated expansion without a cosmological constant. (2) Cosmological perturbations are well behaved. (3) Implementing the model in a Boltzmann code and comparing with observations we find that the RR model fits the CMB, BAO, SNe, structure formation data and local H 0 measurements at a level statistically equivalent to ΛCDM. (4) Bayesian parameter estimation shows that the value of H 0 obtained in the RR model is higher than in ΛCDM, reducing to 2.0σ the tension with the value from local measurements. (5) The RR model provides a prediction for the sum of neutrino masses that falls within the limits set by oscillation and terrestrial experiments (in contrast to ΛCDM, where letting the sum of neutrino masses vary as a free parameter within these limits, one hits the lower bound). (6) Gravitational waves propagate at the speed of light, complying with the limit from GW170817/GRB 170817A.
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Some modified gravity models reduce or alleviate the tension in the Hubble parameter.
“As we discuss further below in some of the sub-sections (see e.g., Sects. 9.7 and 9.9), some authors find that some modified gravity models reduce or alleviate the tension in the Hubble parameter (see e.g., Barreira et al. 2014a; Belgacem et al. 2018b).”
From Testing general relativity in cosmology (2019) · cites this paper as Belgacem et al. 2018b
The ghost-like feature of the field U in this case is only classical, with no associated quanta nor instability when quantizing the theory.
“The good news is that the ghost-like feature of the field in this case is only classical with no associated quanta nor instability when quantizing the theory.”
From Testing general relativity in cosmology (2019) · cites this paper as Belgacem et al. (2018b)
In the minimal nonlocal gravity model, the flatness condition allows one to derive the mass parameter m, as in ΛCDM for the cosmological constant.
“Interestingly, just like for in the CDM model, in the model, the flatness condition allows one to derive the mass parameter m.”
From Testing general relativity in cosmology (2019) · cites this paper as Belgacem et al. (2018b)
The Deser-Woodard model can be adjusted to fit well the background accelerating expansion with no need for a dark energy component, although in a non-predictive way.
“It is possible to adjust their model so it can fit well the background accelerating expansion with no need for a dark energy component (Woodard 2014), although in a non-predictive way state (Belgacem et al. 2018b).”
From Testing general relativity in cosmology (2019) · cites this paper as Belgacem et al. 2018b
The classical instability of the field U is responsible for the observed late-time cosmic acceleration.
“On the contrary, the classical instability is a plus and would be responsible for the observed late-time cosmic acceleration.”
From Testing general relativity in cosmology (2019) · cites this paper as Belgacem et al. (2018b)
The growth of U implies that both the effective dark energy density and its variation are positive, resulting in a phantom effective equation of state caused by the ghost-like field U.
“Moreover, this implies that both the effective dark energy density and its variation are positive resulting in a phantom effective equation of state caused by the ghost-like field U.”
From Testing general relativity in cosmology (2019) · cites this paper as Belgacem et al. (2018b)
In the RR model, the classical instability develops on a cosmological timescale producing late cosmic acceleration with an effective phantom-like dark energy component that is consistent with cosmological background and growth of structure observations.
“In fact, the classical instability develops rather on a cosmological timescale producing the late cosmic acceleration with an effective phantom-like dark energy component that is found to be consistent with cosmological background and growth of structure observations.”
From Testing general relativity in cosmology (2019) · cites this paper as Belgacem et al. (2018b)
Upon quantization, the RR theory remains ghost-free because there are no quanta associated to the two fields U and S.
“However, as discussed in Belgacem et al. (2018b) and references therein, upon quantization, the theory remains ghost-free because there are no quanta associated to these two fields.”
From Testing general relativity in cosmology (2019) · cites this paper as Belgacem et al. (2018b)
The minimal nonlocal gravity model has the same background parameters as the ΛCDM model.
“So the model has the same background parameters as the CDM model.”
From Testing general relativity in cosmology (2019) · cites this paper as Belgacem et al. (2018b)
A choice of boundary conditions for the auxiliary fields U and W can provide a minimal nonlocal gravity model whose background evolution depends on the Hubble constant, the matter density parameter, and one additional parameter m that replaces the cosmological constant.
“As discussed in Maggiore and Mancarella (2014) and Belgacem et al. (2018b), a choice of boundary conditions can be made for the auxiliary fields U and W that can provide a minimal model with a background evolution that depends on the Hubble constant, the matter density parameter , and one additional parameter that is the mass m that replaces the cosmological constant.”
From Testing general relativity in cosmology (2019) · cites this paper as Belgacem et al. (2018b)
For the same fiducial cosmological model, comoving distances in the minimal nonlocal gravity model and ΛCDM can differ by up to 2.5%; if each model is fed its best-fit cosmological parameters, the difference can be brought below 1% up to redshift 6.
“Belgacem et al. (2018b) compared the comoving distances between the minimal model and the CDM and found that for the same values of a fiducial cosmological model these can be different by up to 2.5%, however, if each models is fed its best-fit values of cosmological parameters, the difference can be brought down to below 1% up to redshift 6 (see Fig. 2 there).”
From Testing general relativity in cosmology (2019) · cites this paper as Belgacem et al. (2018b)
In the nonlocal gravity model, the field U is zero in the radiation dominated era and grows in the matter dominated era, causing the effective dark energy density to grow.
“While it is zero in the radiation dominated era, the field U grows in the matter dominated era resulting in the growth of the effective dark energy density as indicated by (279).”
From Testing general relativity in cosmology (2019) · cites this paper as Belgacem et al. (2018b)
Belgacem et al. (2018b) showed that gravitational waves in the non-local model propagate at the speed of light and thus comply with the GW170817/GRB170817A limit.
“They showed that that gravitational waves in the model propagate at the speed of light and thus comply with the limit .”
From Testing general relativity in cosmology (2019) · cites this paper as Belgacem et al. (2018b)
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INCONSISTENCIES FROM A RUNNING COSMOLOGICAL CONSTANT
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<i>Planck</i> 2018 results: VI. Cosmological parameters
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Early Dark Energy can Resolve the Hubble Tension
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Gravitational Rainbows: LIGO and Dark Energy at its Cutoff
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Testing modified gravity at cosmological distances with LISA standard sirens
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Introduction to Quantum Field Theory with Applications to Quantum Gravity
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MOND-like fractional Laplacian theory
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Towards Reconstructing the Quantum Effective Action of Gravity
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Neutrino oscillations in extended theories of gravity
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Gravitational wave constraints on dark sector models
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Gaussian processes reconstruction of modified gravitational wave propagation
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Gravity in the infrared and effective nonlocal models
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Self-citationGravitational-wave detector networks: standard sirens on cosmology and modified gravity theory
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Exorcising ghosts in quantum gravity
Kuntz, I. (2020) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-020-00875-x · Cited by 7 · see citing works
de Souza, J. M. S., & Sturani, R. (2021) · Physics of the Dark Universe · doi:10.1016/j.dark.2021.100830 · Cited by 6 · see citing works
Is there evidence for CIDER in the Universe?
Barros, B. J., Castelão, D., da Fonseca, V., Barreiro, T., Nunes, N., & Tereno, I. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/01/013 · Cited by 4 · see citing works
Giani, L., & Piattella, O. F. (2023) · Physics of the Dark Universe · doi:10.1016/j.dark.2023.101219 · Cited by 6 · see citing works
Graviton-photon oscillation in alternative theories of gravity
Cembranos, J. A. R., Díaz, M. C., & Martín–Moruno, P. (2018) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aae1d9 · Cited by 6 · see citing works
Cosmology and Newtonian limit in a model of gravity with nonlocally interacting metrics
Giani, L., Miranda, T., & Piattella, O. F. (2019) · Physics of the Dark Universe · doi:10.1016/j.dark.2019.100357 · Cited by 6 · see citing works
New regular 2+1 black hole solutions in bilocal gravity
Christiansen, H. R., Estrada, M., Cunha, M. S., Furtado, J., & Muniz, C. R. (2023) · International Journal of Modern Physics D · doi:10.1142/s0218271823500414 · Cited by 6 · see citing works
- Authors
- Belgacem, E., Dirian, Y., Foffa, S., & Maggiore, M.
- Affiliations
- University of Geneva (CH)
- ORCID
- Belgacem, Enis
- Venue
- Journal of Cosmology and Astroparticle Physics
- Publisher
- IOP Publishing
- Published
- 2018-03-05
- Volume
- 2018
- Issue
- 03
- Pages
- 002-002
- ISSN
- 1475-7508 (ISSN-L)
- 1475-7516
- OpenAlex
- W2776650608
- Cited by
- 161
- References
- 95
- Citations by year
- 2026: 8 · 2025: 6 · 2024: 12 · 2023: 12 · 2022: 11 · 2021: 48 · 2020: 23 · 2019: 26 · 2018: 15
- FWCI
- 15.01
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Journal of Cosmology and Astroparticle Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Utrecht University Repository (Utrecht University) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- National Centres of Competence in Research SwissMAP
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- nonlocal gravity, effective action, conformal mode, dark energy, phantom equation of state, cosmic acceleration, cosmological perturbations, Hubble tension, sum of neutrino masses, gravitational wave speed, causality, Boltzmann code
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