REVIEW
Opening up extra dimensions at ultra-large scales
High Energy Physics - Theory · Submitted 9 Feb 2000 · 7 references
Pith's verdict: A clean, correct linearized calculation showing the graviton is only partially localized in the CGR three-brane model, with a genuine 1/r^2 regime beyond r_c = k^{-1}e^{3kz_c}; the soft spots are the radion-stabilization hedge and an unproved no-ghost claim.
T0 · AI review
Why Pith says this
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Referee report
The paper
The paper claims
Gravity may become five-dimensional again at ultra-large distances, with ordinary four-dimensional gravity holding only in between.
The reading
What carries the argument
The load-bearing object is the continuous Kaluza-Klein spectrum of the three-brane background and its collective contribution to the static potential, Eq. (13), split at $m = zeta_c^{-1}$ into a part that dominates at large $r$ and a Randall-Sundrum-like part that gives short-distance corrections. The normalization of the modes in the small-mass regime, $C_m^2 = pi(kzeta_c)^3 (1 + 4(mzeta_c)^2(kzeta_c)^4)^{-1}$, is what converts the mode sum into a Breit-Wigner-like factor with a pole structure of width set by $r_c$; the same factor, continued to finite frequency, produces the error-function form of the wave Green's function and hence the $r^{-3/2}$ leakage law. The mechanism is that the anti-de Sitter sandwich becomes thin compared with the flat region as $z_c$ grows, so the localized mode is only quasilocalized.
Extended reading notes
Core claim
In the three-brane background of Charmousis, Gregory and Rubakov, with a positive-tension brane flanked by two negative-tension branes beyond which the bulk is flat, the linearized graviton has no normalizable zero mode: the spectrum is continuous from $m^2 = 0$. Summing the exchange of these modes between two unit masses on the positive-tension brane gives a static potential that equals $G_N/r$ for $k^{-1}ll rll r_c$ and crosses over to $G_N r_c/(pi r^2)$ for $rgg r_c$, with $r_c = k^{-1}e^{3kz_c}$. So the extra dimension opens up at short distances, closes over an intermediate window, and opens again at ultra-large distances, where the effective five-dimensional Newton constant is renormalized relative to $G_5$. The same incomplete localization makes the would-be four-dimensional graviton metastable: its width is of order $r_c^{-1}$, and a gravitational wave of frequency $omega$ keeps its four-dimensional $1/r$ amplitude only out to $r sim omega r_c^2$, beyond which the amplitude falls as $r^{-3/2}$ and energy is lost into the fifth dimension.
Load-bearing premise
The static-potential result assumes the distance between the branes is stabilized, since an unstabilized radion has zero four-dimensional mass and would add a $1/r$ scalar force that dominates over the claimed $1/r^2$ tensor behavior at large distances; the paper notes this and cites a stabilization mechanism but does not supply one.
Editorial extensions
If this is right
- Newton's law survives from $k^{-1}$ out to $r_c = k^{-1}e^{3kz_c}$; with $k sim M_{Pl}$ and $z_c sim 50$ Planck lengths, $r_c sim 10^{28}$ cm, the present horizon.
- Beyond $r_c$ the potential becomes $G_N r_c/(pi r^2)$, a five-dimensional law with a renormalized gravitational constant rather than the microscopic $G_5$.
- Long-distance corrections to Newton's law, of relative size $r/r_c$ times a logarithm, overtake the short-distance corrections at $r sim zeta_c$, which in the worked example is around $10^{-13}$ cm.
- Gravitational waves from a periodic source lose amplitude into the fifth dimension beyond $r sim omega r_c^2$, so four-dimensional energy conservation fails for brane observers at sufficiently large distances.
- Compactifying the fifth dimension at a radius $z_* gg z_c$ discretizes the spectrum and restores a true zero mode, so five-dimensional gravity would hold only in a finite window before four-dimensional behavior returns at the very largest scales.
Reading between the lines
- The construction suggests a general design rule for brane worlds: any model whose localized graviton is merely metastable inherits a finite range of four-dimensional validity, with the range set by the inverse width of the resonance rather than by the brane separation itself.
- Because $r_c$ depends exponentially on $z_c$, a modest change in brane spacing moves the crossover across many orders of magnitude, which makes the scenario unusually sensitive to whatever fixes the inter-brane distance in an underlying theory.
- The predicted $r^{-3/2}$ amplitude falloff for distant gravitational waves is a qualitatively different signature from ordinary dilution, and it is the kind of thing that grows more testable as the distance and frequency range of gravitational-wave observations expands.
- If the crossover scale were near the horizon, the effective gravitational coupling would become scale-dependent at cosmological separations, which is the regime where modifications of gravity are often invoked to explain large-scale dynamics.
Original abstract
The standard picture of viable higher-dimensional theories is that extra dimensions manifest themselves at short distances only, their effects being negligible at scales larger than some critical value. We show that this is not necessarily true in models with infinite extra dimensions. As an example, we consider a five-dimensional scenario with three 3-branes in which gravity is five-dimensional both at short {\it and} very long distance scales, with conventional four-dimensional gravity operating at intermediate length scales. A phenomenologically acceptable range of validity of four-dimensional gravity extending from microscopic to cosmological scales is obtained without strong fine-tuning of parameters.
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.
The abstract, sentence by sentence
The standard picture of viable higher-dimensional theories is that extra dimensions manifest themselves at short distances only, their effects being negligible at scales larger than some critical value. We show that this is not necessarily true in models with infinite extra dimensions. As an example, we consider a five-dimensional scenario with three 3-branes in which gravity is five-dimensional both at short {\it and} very long distance scales, with conventional four-dimensional gravity operating at intermediate length scales. A phenomenologically acceptable range of validity of four-dimensional gravity extending from microscopic to cosmological scales is obtained without strong fine-tuning of parameters.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The standard picture of viable higher-dimensional theories is that extra dimensions manifest themselves at short distances only, their effects being negligible at scales larger than some critical value. | background 1.00 | 0.03 | 0.03 | asserted 0.99 |
| s1 | We show that this is not necessarily true in models with infinite extra dimensions. | contribution 0.50 | 0.86 | 0.68 | asserted 0.87 |
| s2 | As an example, we consider a five-dimensional scenario with three 3-branes in which gravity is five-dimensional both at short {\it and} very long distance scales, with conventional four-dimensional gravity operating at intermediate length scales. | contribution 0.50 | 0.83 | 0.30 | asserted 0.98 |
| s3 | A phenomenologically acceptable range of validity of four-dimensional gravity extending from microscopic to cosmological scales is obtained without strong fine-tuning of parameters. | result 0.95 | 0.88 | 0.24 | asserted 0.98 |
What was examined, and what was not
- arXiv listing abstract v2
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References
How later papers used it
51 later papers cite it
2 later papers by other authors are listed below: 2 used its method or tool.
Uses its method or tool 2 of 4 papers with this label
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Defined the width of a resonant state as the width at the half maximum of a resonant peak, citing this paper.
Fermion Resonances on a Thick Brane with a Piecewise Warp Factor (2010) · 0.83 · paraphrased: the licence does not allow quoting
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Estimated the lifetime as the inverse of the full width at half maximum of the peak, as in this paper.
Localization and quasilocalization of spin-$1/2$ fermion field on two-field thick braneworld (2014) · 0.95 · paraphrased: the licence does not allow quoting
How the literature uses it
49 arXiv papers cite this in 59 sentences
Papers citing it · 21 sentences without a confident label
Uses its method or tool 3 papers
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To further analyze the lifetime of a fermion resonance, first, we define the width $Γ=Δm$ of a resonant state as the width at the half maximum of a resonant peak [ref] .
Fermion Resonances on a Thick Brane with a Piecewise Warp Factor · Case I: $k$ as a variable · 0.83
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The life-time $τ$ of a resonant mode can obtained by $τ=1/Γ$, where $Γ$ is the full width at half maximum (FWHM) [ref] .
Localization of matter fields on a chameleon brane · Quasi-localiztion of $q$-form fields · 0.85
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As in Ref. [ref] , the lifetime $τ$ is estimated to $τ∼Γ^-1$, with $Γ=δm$ being the full width at half maximum of the peak.
Localization and quasilocalization of spin-$1/2$ fermion field on two-field thick braneworld · Localization of a bulk fermion on the brane · 0.95
Compares with it 3 papers
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So, we have a situation similar to [ref] where the tachyons and ghosts can be present.
Softly higher-derivative massive gravity · Final Remarks · 1.00
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It should be pointed out that our boundary condition [ref] is consistent with those obtained by the $ℤ_2$ orbifold picture [ref] , which is consistent with Israel junction condition [ref] , and by the variational principle with the Gibbons-Hawking extrinsic curvature terms [ref] at $z=z_1$ and $z_2$ [ref] .
SUSY QM Meets 5d Gravity · Boundary conditions and SUSY · 0.89
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Analogous effect was observed in Ref. [ref] within the framework of modified Randall-Sundrum model, which also contains the metastable effective graviton on the brane.
Leakage of gravitational waves into an extra dimension in the DGP model · Conclusions · 0.95
Cites it as background 31 papers
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In particular, $δ$-like branes[Sometimes also called thin branes.] [ref] , i.e. zero-thickness hypervolumes, are used to localize lower-dimensional fields on their worldvolumes.
Comment on "Braneworld Effective Field Theories -- Holography, Consistency and Conformal Effects" · Introduction · 0.92
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Perhaps the most notable examples of this approach are braneworld modifications [ref] and theories with new scalars disguised as $f(R)$ terms [ref] .
A New Perspective on DGP Gravity · Introduction · 0.97
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On the base of the RS model, another model called the Gergory-Rubakov-Sibiryakov (GRS) model was proposed [ref] , in order to give some modifications of gravity at ultralarge scales.
Bulk Matters on a GRS-Inspired Braneworld · Introduction · 0.92
Discussion
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