Effective Nonlocal Euclidean Gravity

C. Wetterich

RECORD

Effective Nonlocal Euclidean Gravity

C. Wetterich

General Relativity and Quantum Cosmology · Submitted 18 Apr 1997

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action.

how it is stated · hedged possibility 1.00 read the record →

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.94 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.36 · compares with prior results 0.29 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action. On sub-horizon length scales the modified gravitational field equations seem compatible with all present tests of general relativity and post-Newtonian gravity. They induce a difference in the effective Newton's constant between regions of space with vanishing or nonvanishing curvature scalar (or Ricci tensor). In cosmology they may lead to a value $\Omega<1$ for the critical density after inflation. The simplest model considered here appears to be in conflict with nucleosynthesis, but generalizations consistent with all cosmological observations seem conceivable.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action.	contribution 0.41	0.24	0.68	hedged possibility 1.00
s1	On sub-horizon length scales the modified gravitational field equations seem compatible with all present tests of general relativity and post-Newtonian gravity.	result 0.94	0.67	0.10	hedged possibility 0.96
s2	They induce a difference in the effective Newton's constant between regions of space with vanishing or nonvanishing curvature scalar (or Ricci tensor).	result 0.95	0.72	0.10	asserted 0.98
s3	In cosmology they may lead to a value $\Omega<1$ for the critical density after inflation.	result 0.53	0.59	0.08	hedged possibility 1.00
s4	The simplest model considered here appears to be in conflict with nucleosynthesis, but generalizations consistent with all cosmological observations seem conceivable.	limitation 1.00	0.78	0.12	hedged possibility 0.40

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.62.

What was examined, and what was not

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arXiv listing abstract v1

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full text
figures and tables
references and citing sentences
relations to other papers

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P abstract

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S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action. On sub-horizon length scales the modified gravitational field equations seem compatible with all present tests of general relativity and post-Newtonian gravity. They induce a difference in the effective Newton's constant between regions of space with vanishing or nonvanishing curvature scalar (or Ricci tensor). In cosmology they may lead to a value $\Omega<1$ for the critical density after inflation. The simplest model considered here appears to be in conflict with nucleosynthesis, but generalizations consistent with all cosmological observations seem conceivable.

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References

Forward citations

Cited by 9 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Generalised Quadratic Curvature, Non-Local Infrared Modifications of Gravity and Newtonian Potentials
hep-th 2014-06 conditional novelty 6.0 of 10

A general algorithm maps any quadratic-curvature non-local gravity action to its Newtonian potentials, and a new exponential-of-inverse-d'Alembertian model yields a potential that decays in the far infrared.
On the renormalization group flow of f(R)-gravity
hep-th 2007-12 conditional novelty 6.0 of 10

Including ln(R) and R^{-n} terms in the gravitational effective action removes the infrared singularity at lambda = 1/2 and, for the ln(R) case, produces an infrared fixed point that drives the cosmological constant to zero.
Nonlocal Cosmology
astro-ph 2007-06 conditional novelty 6.0 of 10

Nonlocal terms built from the retarded inverse d'Alembertian of the Ricci scalar can, with order-unity couplings, produce a delayed onset of cosmic acceleration at roughly the observed redshift.
The Running Gravitational Couplings
hep-th 1997-07 conditional novelty 6.0 of 10

Using a truncated exact renormalization group for gravity plus matter of all spins, the authors find Newton's constant barely runs while the cosmological constant scales like the fourth power of the cutoff at high ene...
Nonlocal Gravity, Restricted CPL Dynamics and DESI Constraints
astro-ph.CO 2026-10 accept novelty 5.0 of 10

Current cosmological data constrain the Maggiore-Mancarella nonlocal gravity model to be indistinguishable from Lambda-CDM, ruling out significant nonlocal deviations.

Show 4 more citing papers

Testing modified gravity at cosmological distances with LISA standard sirens
astro-ph.CO 2019-06 conditional novelty 5.0 of 10

Mock LISA catalogs of supermassive black hole mergers, combined with CMB, BAO and supernova data, would constrain a modified-gravity parameter controlling the gravitational-wave distance to roughly 1 to 4 percent.
Observational Viability and Stability of Nonlocal Cosmology
astro-ph.CO 2013-07 conditional novelty 5.0 of 10

The Deser-Woodard nonlocal gravity model is shown to have the same degrees of freedom and constraints as general relativity, to be ghost-free, and to be screenable in bound systems, though a note in proof concedes ten...
Nonlocal gravity. Conceptual aspects and cosmological predictions
hep-th 2017-12 conditional novelty 4.0 of 10

The RR nonlocal-gravity model fits current cosmological data about as well as ΛCDM while yielding a higher Hubble constant and a nonzero neutrino mass sum, though that mass sum is a fitted parameter rather than a prediction.
Nonlocal Models of Cosmic Acceleration
astro-ph.CO 2014-01 accept novelty 3.0 of 10

Nonlocal gravity can reproduce the cosmic expansion history without dark energy and without solar-system screening, but the simplest models are ruled out by structure growth data.

How the literature uses it

24 arXiv papers cite this in 38 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 26 sentences without a confident label

Contests it 2 papers

A nonlocal gravity model based on this idea was proposed in [ref] (see also [ref] for earlier work), but is now ruled out [ref] .

Nonlocal gravity and gravitational-wave observations · The RT nonlocal gravity model · contest 0.84
The model, however, did not produce a viable cosmological evolution [ref] .

Gravity in the infrared and effective nonlocal models · Difficulties of alternative nonlocal models · contest 0.86

Builds on it 1 paper

Our Letter complements the results in [ref] by accounting for non-local higher derivative terms, the latter being of relevance in several quantum gravity models [ref] , black hole physics [ref] , and cosmology [ref] .

Diverging black hole entropy from quantum infrared non-localities · Introduction · 0.88

Uses its method or tool 1 paper

One minimal way of eliminating inessential couplings within the FRG has been introduced in [ref] , and is based on an appropriate $k$-dependent field redefinition at the level of the flow equation, [equation] This equation is based on a more general flow equation [ref] , see [ref] for earlier applications.

Unearthing the intersections: positivity bounds, weak gravity conjecture, and asymptotic safety landscapes from photon-graviton flows · The Functional Renormalization Group · 0.98

Cites it as background 8 papers

The first nonlocal mechanism for cosmic acceleration was proposed by Deser and Woodard (DW) [ref] (see Ref. [ref] for a review),[Strictly speaking, the cosmology of nonlocal models was proposed and studied first in Ref. [ref] for models with similar structures, although with no connection to cosmic acceleration, which was not yet discovered at the time.] where a simple term of the form $Rf(1/R)$ was added to the standard Einstein-Hilbert term in GR.

On nonlocally interacting metrics, and a simple proposal for cosmic acceleration · Introduction · 0.99
Following this approach, many non-local extensions of GR have been proposed in literature [ref] .

Testing non-local gravity through Ultra-Diffuse Galaxies kinematics · Non-local gravity · 0.95
Models have also been proposed in a bottom-up approach for appreciating the effects of various types of nonlocal operators within the cosmological context [ref] .

Changing the prior: absolute neutrino mass constraints in nonlocal gravity · Introduction · 0.85

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