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Non-Local Modification of Gravity and the Cosmological Constant Problem

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ReviewThe objections and verdict, as JSON Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Nima Arkani-Hamed, Savas Dimopoulos, Gia Dvali, Gregory Gabadadze

High Energy Physics - Theory · Submitted 26 Sep 2002 · 17 references

Pith's verdict: A clean, honest phenomenological proposal: the single-term averaged-curvature equation and the inflation self-termination idea are the real contributions, but the existence of the claimed dS solution is assumed rather than shown.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

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  4. T3 Formal statement The claims written out in a formal math language a computer can read.
  5. T4 Proof Those claims proved, and the proof checked by computer.

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arXiv IDhep-th/0209227 (version 1)
Pith IDRIDXUKO3, Pith's permanent record of this paper and its review
CitationGia Dvali, Gregory Gabadadze, Nima Arkani-Hamed, Savas Dimopoulos. "Non-Local Modification of Gravity and the Cosmological Constant Problem." arXiv:hep-th/0209227 (2002). https://pith.science/paper/RIDXUKO3
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The paper

The paper claims

A non-local, acausal modification of Einstein's equations suppresses the gravitational effect of vacuum energy at cosmological distances while leaving local physics unchanged.

The reading

The cosmological constant problem is the mismatch between the enormous vacuum energy predicted by quantum field theory and the tiny observed curvature of the universe. This paper takes a different tack from most approaches: instead of trying to make the vacuum energy small, it modifies gravity so that energy spread uniformly over enormous distances and times barely gravitates at all. The authors propose replacing Einstein's equation with a version that includes a filter function depending on a scale L. For sources varying rapidly in space or time, the filter switches off and ordinary general relativity is recovered. For sources that are uniform over scales larger than L, such as the vacuum energy, the effective Newton constant becomes tiny. In the limit L goes to infinity, the modification reduces to a single extra term proportional to the spacetime-averaged Ricci curvature, with a new mass scale M-bar that must be enormous (around 10^48 GeV for a TeV-scale vacuum energy). The paper argues that this construction leaves stars, galaxies, and standard cosmology unaffected, and it sketches a new picture in which inflation ends naturally when the expansion stretches the relevant wavelengths past L. The authors are explicit that the modification is non-local and acausal, and that they do not derive it from a fundamental theory.
Extended reading notes

Core claim

In the L to infinity limit, the modified Einstein equation M_Pl^2 G_munu - (1/4) M-bar^2 g_munu R-bar = T_munu (Eq. 8) suppresses the curvature produced by a vacuum energy E to R = -4E/(M_Pl^2 + M-bar^2), which can be made acceptably small by taking M-bar large, without fine-tuning E or M-bar. The paper argues this modification preserves all local gravitational physics because R-bar vanishes for stars, black holes, and matter- or radiation-dominated FRW universes.

Load-bearing premise

The spacetime average R-bar defined in Eq. (9) is well-defined and, for the universes of interest, dominated by the asymptotic de Sitter future. The paper itself acknowledges that the integrals can diverge in infinite spacetimes or near curvature singularities, that the prescription must be supplemented by excising Planckian-curvature regions, and that more general prescriptions may be needed. The entire suppression mechanism rests on this definition being meaningful and on the deep future dominating the average.

Original abstract

We propose a phenomenological approach to the cosmological constant problem based on generally covariant non-local and acausal modifications of four-dimensional gravity at enormous distances. The effective Newton constant becomes very small at large length scales, so that sources with immense wavelengths and periods -- such as the vacuum energy-- produce minuscule curvature. Conventional astrophysics, cosmology and standard inflationary scenaria are unaffected, as they involve shorter length scales. A new possibility emerges that inflation may ``self-terminate'' naturally by its own action of stretching wavelengths to enormous sizes. In a simple limit our proposal leads to a modification of Einstein's equation by a single additional term proportional to the average space-time curvature of the Universe. It may also have a qualitative connection with the dS/CFT conjecture.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. 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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,876 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.40 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.05 · 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; .

We propose a phenomenological approach to the cosmological constant problem based on generally covariant non-local and acausal modifications of four-dimensional gravity at enormous distances. The effective Newton constant becomes very small at large length scales, so that sources with immense wavelengths and periods -- such as the vacuum energy-- produce minuscule curvature. Conventional astrophysics, cosmology and standard inflationary scenaria are unaffected, as they involve shorter length scales. A new possibility emerges that inflation may ``self-terminate'' naturally by its own action of stretching wavelengths to enormous sizes. In a simple limit our proposal leads to a modification of Einstein's equation by a single additional term proportional to the average space-time curvature of the Universe. It may also have a qualitative connection with the dS/CFT conjecture.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We propose a phenomenological approach to the cosmological constant problem based on generally covariant non-local and acausal modifications of four-dimensional gravity at enormous distances. contribution 0.99 0.80 0.24 asserted 0.75
s1 The effective Newton constant becomes very small at large length scales, so that sources with immense wavelengths and periods -- such as the vacuum energy-- produce minuscule curvature. result 0.51 0.47 0.29 asserted 0.99
s2 Conventional astrophysics, cosmology and standard inflationary scenaria are unaffected, as they involve shorter length scales. interpretation 0.51 0.22 0.06 asserted 1.00
s3 A new possibility emerges that inflation may ``self-terminate'' naturally by its own action of stretching wavelengths to enormous sizes. interpretation 0.94 0.32 0.11 hedged possibility 0.99
s4 In a simple limit our proposal leads to a modification of Einstein's equation by a single additional term proportional to the average space-time curvature of the Universe. result 0.61 0.82 0.25 asserted 0.49
s5 It may also have a qualitative connection with the dS/CFT conjecture. interpretation 0.98 0.16 0.04 hedged possibility 0.99

What kind of paper the classifier reports this is: theoretical result 0.74 · evidence from argument 0.95.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • 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

References
How later papers used it

107 later papers cite it

Evidence: some. 103 of the citing papers share no author with it, and 3 of those carry a confident label from Pith's citation classifier.

Pith read 16 of the 146 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 1 paper
How the literature uses it

108 arXiv papers cite this in 148 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 · 95 sentences without a confident label

Uses its method or tool 1 paper
Compares with it 3 papers
  • The nonlocality here reminds one at once the one arising in [ref] ; however, one notices that dynamical structure here is entirely different in regard to ([ref]).

    Vacuum Energy as the Origin of the Gravitational Constant · An Alternative Route · 0.99

  • The momentum dependence of $G$ (that contributes to graviton decay and a varying gravitational coupling) does not play any role in this, in contrast to the more general “filter” mechanisms of [ref] * It also follows that at large distances ($k^2→0$), the behaviour of gravity does not become higher dimensional, unlike the $n=1$ DGP model.

    Brane Induced Gravity, its Ghost and the Cosmological Constant Problem · Filtering out of brane cosmological constant · 0.83

  • In the context of inflationary cosmology, the present method would remove a constant piece from the inflationary potential, while retaining all the positive aspects of the slow-roll inflationary paradigm (note a similarity in this with Ref. [ref] ).

    General Relativity With An Auxiliary Dimension · 2. Equations, Solutions and Boundary Terms · 0.98

Cites it as background 46 papers
  • The degravitation paradigm [ref] [ref] [ref] is a phenomenological proposal designed to solve the cosmological constant (CC) problem directly.

    Degravitation, Inflation and the Cosmological Constant as an Afterglow · Introduction · 0.91

  • These modifications must become important at late times in order to explain the fact that the universe has started to accelerate only recently, and so much attention has been focused on actions with inverse powers of curvature invariants, mainly squares of the Ricci scalar $R$, the Ricci tensor $R_μν$, and the Riemann tensor $R_μνρσ$ [ref] .

    Unsuccessful cosmology with Modified Gravity Models · Introduction · 0.90

  • The first successful model of this type was proposed in [ref] (see also [ref] for earlier related ideas), and is defined by the non-local equation of motion -m^2/3\(R\)^T=8πG , where the superscript T denotes the operation of taking the transverse part of a tensor (which is itself a non-local operation).

    Perturbative loop corrections and nonlocal gravity · Introduction · 0.84

Discussion

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