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Accelerated Universe from Gravity Leaking to Extra Dimensions

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Cédric Deffayet, Gia Dvali, Gregory Gabadadze

Astrophysics · Submitted 4 May 2001 · 30 references

Pith's verdict: The mechanism is imported from Ref. [6]; what's new here is the observational confrontation and the no-go for 4D mimicry — and the one load-bearing gap is the vDVZ resolution deferred to a paper in preparation.

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 IDastro-ph/0105068 (version 1)
Pith ID4X5ZPBI3, Pith's permanent record of this paper and its review
CitationC\'edric Deffayet, Gia Dvali, Gregory Gabadadze. "Accelerated Universe from Gravity Leaking to Extra Dimensions." arXiv:astro-ph/0105068 (2001). https://pith.science/paper/4X5ZPBI3
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The paper

The paper claims

The Universe's acceleration might come from gravity leaking into a fifth dimension, not from a cosmological constant.

The reading

This paper argues that the observed speeding-up of cosmic expansion need not come from a small vacuum energy. Instead, ordinary particles live on a three-dimensional sheet (a brane) inside an infinite fifth dimension, and gravity is four-dimensional only at short range; beyond a crossover distance $r_c$ it spreads into the bulk and weakens. If $r_c$ is chosen to be roughly today's Hubble radius, the modified expansion law on the brane contains a branch that accelerates on its own, with no matter and no cosmological constant on the brane. The authors show this branch reproduces the supernova dimming while predicting an effective dark-energy equation of state slightly above $-1$, and they argue the behaviour cannot be faked by any local four-dimensional modification of gravity.

What carries the argument

The load-bearing object is the crossover scale $r_c = M_{Pl}^2/(2 M_{(5)}^3)$, set by competition between the induced four-dimensional Einstein-Hilbert term on the brane and the five-dimensional bulk term. It controls both the static force law, which runs from $1/r$ to $1/r^2$ at $r ~ r_c$, and the expansion history through the modified Friedmann equation. In momentum space the brane propagator behaves as $1/(M_{Pl}^2 p^2 + 2 M_{(5)}^3 p)$, which the authors note corresponds in position space to a nonlocal operator $-partial^2 + sqrt(-partial^2)/r_c$; no ordinary four-dimensional field theory with finitely many bosons produces this. A second piece of machinery is the coordinate transformation showing the bulk metric of the cosmological solution is flat Minkowski space, with the brane appearing as a hyperboloid boundary condition.

Extended reading notes

Core claim

The central claim is that the five-dimensional brane-world model with an induced four-dimensional Ricci scalar on the brane contains a self-inflationary cosmological solution. The modified Friedmann equation reads $H^2 + k/a^2 = (sqrt(rho/(3 M_{Pl}^2) + 1/(4 r_c^2)) + epsilon/(2 r_c))^2$, and on the branch $epsilon = +1$ with $rho = 0$ it gives $H = 1/r_c$. The brane's own curvature term acts as a source for the bulk and drives the expansion, so the acceleration is a gravitational-leakage effect rather than a vacuum-energy effect. Setting $r_c$ of order the present Hubble radius, equivalently $M_{(5)} ~ 10$–$100$ MeV, puts the onset of acceleration at the observed epoch. The authors then confront this with supernova luminosity distances, the Alcock-Paczynski test, and the position of the first acoustic peak, finding that the model mimics a dark-energy component with $w_X > -1$ rather than an exact cosmological constant.

Load-bearing premise

The model survives short-distance gravity tests only if the extra scalar mode of the flat-space propagator is screened nonperturbatively, and that screening is asserted here by appeal to an earlier paper and to a follow-up listed as in preparation rather than demonstrated in this text.

Editorial extensions

If this is right

  • If $r_c$ is of order the Hubble radius, the acceleration of the Universe begins at the observed epoch without any vacuum energy on the brane.
  • The expansion history mimics dark energy with equation of state above $-1$, so future luminosity-distance, Alcock-Paczynski, and cosmic-microwave-background measurements can in principle separate it from a cosmological constant.
  • The scenario cannot be reproduced by adding local higher-derivative curvature terms to four-dimensional gravity, because matching it would require a fractional power of the d'Alembertian.
  • The five-dimensional Planck mass can be as low as $10$–$100$ MeV without conflict, since heavy bulk graviton modes are repelled from the brane and high-energy graviton emission stays at the negligible four-dimensional rate.
  • The de Sitter phase seen by brane observers is not eternal: Hawking radiation at temperature $T ~ H$ leaks into the bulk, giving a decay time of order $10^{137}$ s, after which the brane metric approaches Minkowski space.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The model does not remove the coincidence problem so much as relocate it: $r_c$ is put in by hand at today's Hubble radius, and nothing in the dynamics explains why the crossover and the onset of acceleration should coincide with the present epoch.
  • Because the brane's de Sitter phase slowly drains into bulk gravitons, the effective dark energy should drift with time; a redshift-drift measurement of $H(z)$ is the natural place this would show up as a departure from a pure constant.
  • The sign choice $epsilon = pm 1$ is a genuine branch ambiguity: the $epsilon = -1$ branch gives a non-accelerating five-dimensional expansion, so the whole acceleration story rests on the Universe sitting on the accelerating branch.
  • The nonlocal $sqrt(-partial^2)$ structure in the effective four-dimensional description suggests that gravitational-wave propagation and the gravitational slip between potentials could differ from general relativity in this model, which is a separate handle from the expansion history.
Original abstract

We discuss the idea that the accelerated Universe could be the result of the gravitational leakage into extra dimensions on Hubble distances rather than the consequence of non-zero cosmological constant.

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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,613 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.23 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We discuss the idea that the accelerated Universe could be the result of the gravitational leakage into extra dimensions on Hubble distances rather than the consequence of non-zero cosmological constant.

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 discuss the idea that the accelerated Universe could be the result of the gravitational leakage into extra dimensions on Hubble distances rather than the consequence of non-zero cosmological constant. contribution 0.82 0.26 0.58 hedged possibility 0.99

What kind of paper the classifier reports this is: position or commentary 0.81 · evidence from argument 0.99.

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

Figures
Figure 1. Different possibilities for the expansion as a function of Ω
Figure 2. Luminosity distance as a function of red-shift for ordinar
Figure 3. Plot of dL(z)/dref L (z) for various models of dark energy with constant equation of state parameters wX in standard cosmology (solid lines) as compared with the outcome of the model consider in this paper (dashed and dotted lines). All plots correspond to flat universes with ΩM = 0.3 (solid lines, and dotted line), and ΩM = 0.27 (dashed line). 11
Figure 4. Plot of H(z)dC(z)/Href (z)d ref C (z) (Alcock-Paczynski test) for various models of dark energy with constant equation of state parameters wX in standard cosmology (solid lines) as compared with the outcome of the model considered in this paper (dashed and dotted lines). All plots correspond to flat universes, with ΩM = 0.3 (solid lines, and dotted line), and ΩM = 0.27 (dashed line). 4.3 Cosmic Microwave Background (CMB) It is well known that in standard cosmology, the location of points of constant luminosity distance at small z is degenerated in the plane (ΩM, ΩΛ). This degeneracy…
Figure 5. The Solid lines are lines of equal luminosity distance (in our mod
Figure 6. Angular diameter distance dA at z = 1100 of standard cosmology divided by ˜dA(z = 1100) in our model, as a function of wX for a flat universe and ΩM = 0.3 13

Figures reproduced from arXiv:astro-ph/0105068 by the authors.

References
How later papers used it

122 later papers cite it

Evidence: substantial. 114 of the citing papers share no author with it, and 7 of those carry a confident label from Pith's citation classifier.

Pith read 11 of the 144 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

Compares with it 1 of 7 papers with this label

  • Said that with the cosmological constant switched off, its approach yields an accelerated universe behaviour similar to the one developed in this paper.

    Modified geodetic brane cosmology (2011) · 0.81 · paraphrased: the licence does not allow quoting

How the literature uses it

110 arXiv papers cite this in 131 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 · 55 sentences without a confident label

Compares with it 7 papers
  • Clearly, expression ([ref]) specializes to the Friedmann equation found in [ref] for the analysis of an accelerated universe without cosmological constant.

    Modified geodetic brane cosmology · DGP like behaviour from modified GBG cosmology · 0.98

  • So, the present particle creation model which simultaneously fits the observational data and alleviates the coincidence and fine-tuning problems, is better compared to the known (one-parameter) models namely (i) the concordance $Λ$CDM which however suffers from the coincidence and fine-tuning problems [ref] and (ii) the brane world cosmology [ref] which does not fit the SNIa+ BAO+ CMB (shift-parameter) data [ref] .

    Will there be future deceleration? A study of particle creation mechanism in non-equilibrium thermodynamics · Introduction · 0.85

  • This is reminiscent of the situation in the Dvali-Gabadadze-Porrati (DGP) model [ref] , where one branch of solutions has self-accelerating cosmological expansion [ref] but is plagued by a ghost [ref] , while the other branch is healthy but cannot account for cosmic acceleration.

    Massive mimetic cosmology · Cosmological solutions · 0.89

Cites it as support 1 paper
  • It can be shown that this action allows to account for an accelerated expansion of spacetime [ref] (at least as long as de Sitter metric can be viewed as a small deviation from Minkowski spacetime).

    Compact astrophysical objects in modified gravity · Cubic Lagrangian · 0.96

Cites it as background 61 papers
  • In this paper, we will study three different modified gravity scenarios, focusing on their predictions for lensing observables: (i) $$ gravity [ref] ; (ii) the Dvali-Gabadadze-Porrati (DGP) model [ref] ; and (iii) Tensor-Vector-Scalar theory (TeVeS) [ref] .

    Weak Lensing Probes of Modified Gravity · Introduction · 0.82

  • Initially introduced in the context of the DGP model [ref] and later proposed formally as a generic local infrared modification of General Relativity in order to explain the late-time accelerated expansion, Galileons are a defined by introducing an extra scalar degree of freedom, $π$, kinetically mixed with GR [ref] .

    Defrosting in an Emergent Galileon Cosmology · Introduction · 0.98

  • 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

Discussion

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