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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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In the citing paper
“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
In the citing paper
“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 citing paper
“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)
In the citing paper
“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
In the citing paper
“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)
In the citing paper
“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 citing paper
“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)
In the citing paper
“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)
In the citing paper
“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)
In the citing paper
“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)
In the citing paper
“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 citing paper
“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)
In the citing paper
“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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Taming the Beast: Diffusion Method in Nonlocal Gravity
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Newtonian approximation and possible time-varying G in nonlocal gravities
Tian, S., & Zhu, Z. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.064044 · Cited by 14
Form Factors in Asymptotically Safe Quantum Gravity
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Ultraviolet complete dark energy model
Narain, G., & Li, T. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.97.083523 · Cited by 12
Probing alternative cosmologies through the inverse distance ladder
Lindner, M., Max, K., Platscher, M., & Rezacek, J. (2020) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2020/10/040 · Cited by 12
Quantum nonlocality in extended theories of gravity
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No-boundary solutions are robust to quantum gravity corrections
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Spacetime instability due to quantum gravity
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Non-local gravity in bouncing cosmology scenarios
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Electrovacuum solutions in nonlocal gravity
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New regular 2+1 black hole solutions in bilocal gravity
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Metadata
- 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 › Nuclear and High Energy 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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