Evolution of Cosmological Perturbations in the Brane World

Jiro Soda; Kazuya Koyama

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Evolution of Cosmological Perturbations in the Brane World

Kazuya Koyama, Jiro Soda

High Energy Physics - Theory · Submitted 25 May 2000

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

The authors' main claim Using our formalism, the late time evolution of the cosmological scalar perturbations at any scales larger than the AdS curvature scale $l$ is shown to be identical with the one obtained in the conventional 4D cosmology, provided the effect of heavy graviton modes may be neglected.

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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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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,889 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.94 · human participants 0.01 · controlled comparison 0.21 · randomized assignment 0.01 · states quantitative result 0.19 · compares with prior results 0.92 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v6. Results and the main claim are underlined; show every role.

The evolution of the cosmological perturbations is studied in the context of the Randall-Sundrum brane world scenario, in which our universe is realized on a three-brane in the five dimensional Anti-de Sitter(AdS) spacetime. We develop a formalism to solve the coupled dynamics of the cosmological perturbations in the brane world and the gravitational wave in the AdS bulk. Using our formalism, the late time evolution of the cosmological scalar perturbations at any scales larger than the AdS curvature scale $l$ is shown to be identical with the one obtained in the conventional 4D cosmology, provided the effect of heavy graviton modes may be neglected. Here the late time means the epoch when the Hubble horizon $H^{-1}$ in the 4D brane world is sufficiently larger than the AdS curvature scale $l$. If the inflation occurs sufficiently lower than $l^{-1}$, the scalar temperature anisotropies in the Cosmic Microwave Background at large scales can be calculated using the constancy of the Bardeen parameter as is done in the 4D cosmology. The assumption of the result is that the effect of the massive graviton with mass $m e^{-\alpha_0}>l^{-1}$ in the brane world is negligible, where $e^{\alpha_0}$ is the scale factor of the brane world. We also discuss the effect of these massive gravitons on the evolution of the perturbations.

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	The evolution of the cosmological perturbations is studied in the context of the Randall-Sundrum brane world scenario, in which our universe is realized on a three-brane in the five dimensional Anti-de Sitter(AdS) spacetime.	background 0.83	0.42	0.04	asserted 0.91
s1	We develop a formalism to solve the coupled dynamics of the cosmological perturbations in the brane world and the gravitational wave in the AdS bulk.	method 0.59	0.95	0.04	asserted 0.98
s2	Using our formalism, the late time evolution of the cosmological scalar perturbations at any scales larger than the AdS curvature scale $l$ is shown to be identical with the one obtained in the conventional 4D cosmology, provided the effect of heavy graviton modes may be neglected.	result 1.00	0.92	0.81	asserted 0.99
s3	Here the late time means the epoch when the Hubble horizon $H^{-1}$ in the 4D brane world is sufficiently larger than the AdS curvature scale $l$.	interpretation 0.87	0.29	0.04	asserted 0.93
s4	If the inflation occurs sufficiently lower than $l^{-1}$, the scalar temperature anisotropies in the Cosmic Microwave Background at large scales can be calculated using the constancy of the Bardeen parameter as is done in the 4D cosmology.	interpretation 0.67	0.47	0.09	asserted 0.50
s5	The assumption of the result is that the effect of the massive graviton with mass $m e^{-\alpha_0}>l^{-1}$ in the brane world is negligible, where $e^{\alpha_0}$ is the scale factor of the brane world.	limitation 0.99	0.50	0.10	asserted 0.93
s6	We also discuss the effect of these massive gravitons on the evolution of the perturbations.	contribution 0.98	0.81	0.03	unclear 0.88

What kind of paper the classifier reports this is: theoretical result 0.87 · evidence from proof or derivation 1.00.

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arXiv listing abstract v6

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full text
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references and citing sentences
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T body sentences
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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

The evolution of the cosmological perturbations is studied in the context of the Randall-Sundrum brane world scenario, in which our universe is realized on a three-brane in the five dimensional Anti-de Sitter(AdS) spacetime. We develop a formalism to solve the coupled dynamics of the cosmological perturbations in the brane world and the gravitational wave in the AdS bulk. Using our formalism, the late time evolution of the cosmological scalar perturbations at any scales larger than the AdS curvature scale $l$ is shown to be identical with the one obtained in the conventional 4D cosmology, provided the effect of heavy graviton modes may be neglected. Here the late time means the epoch when the Hubble horizon $H^{-1}$ in the 4D brane world is sufficiently larger than the AdS curvature scale $l$. If the inflation occurs sufficiently lower than $l^{-1}$, the scalar temperature anisotropies in the Cosmic Microwave Background at large scales can be calculated using the constancy of the Bardeen parameter as is done in the 4D cosmology. The assumption of the result is that the effect of the massive graviton with mass $m e^{-\alpha_0}>l^{-1}$ in the brane world is negligible, where $e^{\alpha_0}$ is the scale factor of the brane world. We also discuss the effect of these massive gravitons on the evolution of the perturbations.

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References

Forward citations

Cited by 4 Pith papers

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

Mass spectrum of primordial black holes from inflationary perturbation in the Randall-Sundrum braneworld: a limit on blue spectra
astro-ph 2006-03 conditional novelty 6.0 of 10

In a Randall-Sundrum type-2 braneworld, primordial black hole abundances and the diffuse gamma-ray background imply a small-scale scalar spectral index n ≲ 1.3 for ℓ = 0.1 mm and reheating above 10^6 GeV.
Trace anomaly driven inflation
hep-th 2000-10 conditional novelty 6.0 of 10

Matter-field loops dominate the graviton propagator at short wavelengths during anomaly-driven inflation, so short-distance modifications of gravity should leave no imprint on the cosmic microwave background.
Brane-World Gravity
hep-th 2010-04 accept novelty 3.0 of 10

Brane-world models recover four-dimensional gravity at low energies while predicting calculable, testable corrections at high energies, and this review consolidates their geometry, cosmology, and observational status.
Brane cosmology: an introduction
hep-th 2002-09 accept novelty 2.0 of 10

For a mirror-symmetric brane in a five-dimensional bulk, the Friedmann equation becomes H squared proportional to the energy density squared at high energy, reducing to standard cosmology at low energy when the brane ...

How the literature uses it

4 arXiv papers cite this in 4 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

We show that the behavior of cosmological perturbations on superhorizon scales in the brane-world model is the same as that in the standard no-extradimension model, irrespective of the initial condition for bulk perturbations, in the late stage when the cosmic expansion rate $H$ is smaller than the inverse of the bulk curvature scale $\ell$.

Behavior of Cosmological Perturbations in the Brane-World Mode · 0.93

Papers citing it · 1 sentence without a confident label

Cites it as support 1 paper

Since the model we are considering doesn't originate from an exact bulk solution, but rather from a reasonable ansatz for the bulk matter content, a perturbative treatment cannot be particularly helpful. * It turns out that at late times, when the Hubble radius is much greater than the bulk radius of curvature, the results of perturbations appear to be equivalent to those obtained when treating a conventional 4D cosmology [ref] .

Cosmic Acceleration Data and Bulk-Brane Energy Exchange · Introduction · 0.96

Cites it as background 2 papers

Cosmological perturbation theory in braneworld cosmology also has some distinct features [ref] .

Density perturbations in braneworld cosmology and primordial black holes · Introduction · 0.95
The theory of gauge-invariant perturbations in brane-world cosmology has been extensively investigated and developed [ref] and is qualitatively well understood.

Brane-World Gravity · Brane-World Cosmology: Perturbations · 0.91

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