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De Sitter brane-world, localization of gravity, and the cosmological constant
High Energy Physics - Theory · Submitted 29 Nov 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim With these new insights, we show that the localization of a massless 4D graviton as well as the mass hierarchy between $M_{Pl}$ and $M_{Pl (4+n)}$ can be explained in cosmological brane-world models.
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The abstract, sentence by sentence
Cosmological models with a de Sitter 3-brane embedded in a five-dimensional de Sitter spacetime (dS5) give rise to a finite 4D Planck mass similar to that in Randall-Sundrum (RS) brane-world models in AdS5 spacetime. Yet there arise a few important differences as compared to the results with a flat 3-brane or 4D Minkowski spacetime. For example, the mass reduction formula (MRF) $M_{Pl}^2=M_{5}^3 \ell_{AdS}$ as well as the relationship $M_{Pl}^2= M_{Pl(4+n)}^{n+2} L^{n}$ (with $L$ being the average size or the radius of the $n$ extra dimensions) expected in models of product-space (or Kaluza-Klein) compactifications get modified in cosmological backgrounds. In an expanding universe, a physically relevant MRF encodes information upon the four-dimensional Hubble expansion parameter, in addition to the length and mass parameters $L$, $M_{Pl}$ and $M_{Pl (4+n)}$. If a bulk cosmological constant is present in the solution, then the reduction formula is further modified. With these new insights, we show that the localization of a massless 4D graviton as well as the mass hierarchy between $M_{Pl}$ and $M_{Pl (4+n)}$ can be explained in cosmological brane-world models. A notable advantage of having a 5D de Sitter bulk is that in this case the zero-mass wavefunction is normalizable, which is not necessarily the case if the bulk spacetime is anti de Sitter. In spacetime dimensions $D\ge 7$, however, the bulk cosmological constant $\Lambda_b$ can take either sign ($\Lambda_b <0$, $=0$, or $>0$). The D=6 case is rather inconclusive, in which case $\Lambda_b$ may be introduced together with 2-form gauge field (or flux).
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Cosmological models with a de Sitter 3-brane embedded in a five-dimensional de Sitter spacetime (dS5) give rise to a finite 4D Planck mass similar to that in Randall-Sundrum (RS) brane-world models in AdS5 spacetime. | result 0.67 | 0.33 | 0.19 | asserted 1.00 |
| s1 | Yet there arise a few important differences as compared to the results with a flat 3-brane or 4D Minkowski spacetime. | background 0.47 | 0.18 | 0.03 | asserted 0.98 |
| s2 | For example, the mass reduction formula (MRF) $M_{Pl}^2=M_{5}^3 \ell_{AdS}$ as well as the relationship $M_{Pl}^2= M_{Pl(4+n)}^{n+2} L^{n}$ (with $L$ being the average size or the radius of the $n$ extra dimensions) expected in models of product-space (or Kaluza-Klein) compactifications get modified in cosmological backgrounds. | result 0.78 | 0.16 | 0.05 | asserted 0.98 |
| s3 | In an expanding universe, a physically relevant MRF encodes information upon the four-dimensional Hubble expansion parameter, in addition to the length and mass parameters $L$, $M_{Pl}$ and $M_{Pl (4+n)}$. | result 0.72 | 0.43 | 0.06 | asserted 0.99 |
| s4 | If a bulk cosmological constant is present in the solution, then the reduction formula is further modified. | result 0.89 | 0.35 | 0.04 | asserted 0.91 |
| s5 | With these new insights, we show that the localization of a massless 4D graviton as well as the mass hierarchy between $M_{Pl}$ and $M_{Pl (4+n)}$ can be explained in cosmological brane-world models. | result 0.63 | 0.91 | 0.78 | asserted 1.00 |
| s6 | A notable advantage of having a 5D de Sitter bulk is that in this case the zero-mass wavefunction is normalizable, which is not necessarily the case if the bulk spacetime is anti de Sitter. | result 0.64 | 0.57 | 0.12 | asserted 0.97 |
| s7 | In spacetime dimensions $D\ge 7$, however, the bulk cosmological constant $\Lambda_b$ can take either sign ($\Lambda_b <0$, $=0$, or $>0$). | result 0.90 | 0.43 | 0.03 | asserted 0.78 |
| s8 | The D=6 case is rather inconclusive, in which case $\Lambda_b$ may be introduced together with 2-form gauge field (or flux). | result 0.54 | 0.28 | 0.02 | hedged possibility 0.95 |
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The paper
Original abstract
Cosmological models with a de Sitter 3-brane embedded in a five-dimensional de Sitter spacetime (dS5) give rise to a finite 4D Planck mass similar to that in Randall-Sundrum (RS) brane-world models in AdS5 spacetime. Yet there arise a few important differences as compared to the results with a flat 3-brane or 4D Minkowski spacetime. For example, the mass reduction formula (MRF) $M_{Pl}^2=M_{5}^3 \ell_{AdS}$ as well as the relationship $M_{Pl}^2= M_{Pl(4+n)}^{n+2} L^{n}$ (with $L$ being the average size or the radius of the $n$ extra dimensions) expected in models of product-space (or Kaluza-Klein) compactifications get modified in cosmological backgrounds. In an expanding universe, a physically relevant MRF encodes information upon the four-dimensional Hubble expansion parameter, in addition to the length and mass parameters $L$, $M_{Pl}$ and $M_{Pl (4+n)}$. If a bulk cosmological constant is present in the solution, then the reduction formula is further modified. With these new insights, we show that the localization of a massless 4D graviton as well as the mass hierarchy between $M_{Pl}$ and $M_{Pl (4+n)}$ can be explained in cosmological brane-world models. A notable advantage of having a 5D de Sitter bulk is that in this case the zero-mass wavefunction is normalizable, which is not necessarily the case if the bulk spacetime is anti de Sitter. In spacetime dimensions $D\ge 7$, however, the bulk cosmological constant $\Lambda_b$ can take either sign ($\Lambda_b <0$, $=0$, or $>0$). The D=6 case is rather inconclusive, in which case $\Lambda_b$ may be introduced together with 2-form gauge field (or flux).
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References
How the literature uses it
17 arXiv papers cite this in 21 sentences
Papers citing it · 9 sentences without a confident label
Cites it as background 11 papers
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A detailed discussion on localization of gravity in five dimensions appears elsewhere [ref] .
Warped compactification to de Sitter space · The effect of brane action · 0.97
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The first scenario is an alternative to compactification where many models have been proposed [ref] .
The Hierarchy Problem and $\mathcal{N} =2$ $\mathcal{D} = 5$ Supergravity · Solving the modified Friedmann equations · 0.97
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In the later two papers [ref] , the author assumes one warped and uncompactified extra dimension $y$ with negative $Λ_5$.
de Sitter Thin Brane Model · Introduction · 0.88
What it cites · 21 sentences without a confident label
Uses the method or tool of 1 paper
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Next we consider the bulk perturbations of the 5D metric, which can be analyzed by considering a wave equation for a master variable $Ω≡Ω(x^μ; ϕ)$ introduced in [ref] .
Scalar perturbations from brane-world inflation · Linearized bulk equation · 0.99
Compares with 7 papers
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This result may be brought to the form given in [ref] [cf. Eq. (49)], applying Euler's hypergeometric transformations.
Localization of Gravity on Brane Embedded in $AdS_5$ and $dS_5$ · Linearized gravity in 5D · 0.97
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Firstly, the cosmological mass reduction formula (cMRF) [equation] is clearly different from that obtained in a static AdS$_5$ brane-world configuration [ref] , for which [equation] Secondly, and perhaps more importantly, no parameter of the action would have to be tuned to keep $Λ_4$ positive.
An Alternative to Compactification · A spatially flat universe · 1.00
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In [ref] a concern was raised, especially, in the dS$_5$ case, that the correction to the gravitational potential due to the massive KK states may dominate for $r < H^-1< ℓ$, leading to a 5 dimensional behavior which is not Newtonian.
Graviton localization and Newton law for a dS_4 brane in 5D bulk · Correction to Newton's law · 0.90
Cites as background 15 papers
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To this end, the Randall-Sundrum (RS) models in 5 dimensions [ref] could be viewed as the simplest brane-world configurations with 1 extra dimension of space.
An Alternative to Compactification · Introduction · 0.95
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To this end, the Randall-Sundrum (RS) models in 5 dimensions [ref] could be viewed as the simplest brane-world configurations with 1 extra dimension of space.
A Large Mass Hierarchy from a Small Extra Dimension · Introduction · 0.95
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Brane-world models with one or more noncompact extra spaces are known to require the trapping of gravitational degrees of freedom on the brane [ref] .
Gravitational potential correction with Gauss-Bonnet interaction · Linearized gravity in 5D · 0.89
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