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Tensor Perturbations from Brane-World Inflation with Curvature Effects
High Energy Physics - Theory · Submitted 27 Aug 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Moreover, the Gauss-Bonnet effect, relative to standard general relativity, will abruptly enhance the tensor-to-scalar ratio and break the standard consistency relation at high energies, which cannot be evaded by invoking the induced gravity effect, even though the induced gravity strength would mildly counterbalance these significant changes at high energies.
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The abstract, sentence by sentence
The brane-world scenario provides an intriguing possibility to explore the phenomenological cosmology implied by string/M theory. In this paper, we consider a modified Randall-Sundrum single brane model with two natural generalizations: a Gauss-Bonnet term in the five-dimensional bulk action as well as an induced gravity term in the four-dimensional brane action, which are the leading-order corrections to the Randall-Sundrum model. We study the influence of these combined effects on the evolution of the primordial gravitational waves generated during an extreme slow-roll inflation on the brane. The background, for the early inflationary era, is then modeled through a de Sitter brane embedded within an anti-de Sitter bulk. In this framework, we show that both effects tend to suppress the Randall-Sundrum enhancement of the amplitude of the tensor perturbations at relatively high energies. Moreover, the Gauss-Bonnet effect, relative to standard general relativity, will abruptly enhance the tensor-to-scalar ratio and break the standard consistency relation at high energies, which cannot be evaded by invoking the induced gravity effect, even though the induced gravity strength would mildly counterbalance these significant changes at high energies. We note that the brane-world model with or without the induced gravity effect fulfills the consistency relation. Finally, we discuss some implications of the observational constraints.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The brane-world scenario provides an intriguing possibility to explore the phenomenological cosmology implied by string/M theory. | background 1.00 | 0.04 | 0.02 | hedged possibility 0.88 |
| s1 | In this paper, we consider a modified Randall-Sundrum single brane model with two natural generalizations: a Gauss-Bonnet term in the five-dimensional bulk action as well as an induced gravity term in the four-dimensional brane action, which are the leading-order corrections to the Randall-Sundrum model. | contribution 0.67 | 0.59 | 0.03 | asserted 0.92 |
| s2 | We study the influence of these combined effects on the evolution of the primordial gravitational waves generated during an extreme slow-roll inflation on the brane. | contribution 0.99 | 0.87 | 0.04 | asserted 0.70 |
| s3 | The background, for the early inflationary era, is then modeled through a de Sitter brane embedded within an anti-de Sitter bulk. | method 0.98 | 0.44 | 0.02 | asserted 0.98 |
| s4 | In this framework, we show that both effects tend to suppress the Randall-Sundrum enhancement of the amplitude of the tensor perturbations at relatively high energies. | result 1.00 | 0.92 | 0.32 | asserted 1.00 |
| s5 | Moreover, the Gauss-Bonnet effect, relative to standard general relativity, will abruptly enhance the tensor-to-scalar ratio and break the standard consistency relation at high energies, which cannot be evaded by invoking the induced gravity effect, even though the induced gravity strength would mildly counterbalance these significant changes at high energies. | result 0.99 | 0.88 | 0.54 | asserted 0.98 |
| s6 | We note that the brane-world model with or without the induced gravity effect fulfills the consistency relation. | result 0.94 | 0.66 | 0.09 | asserted 0.99 |
| s7 | Finally, we discuss some implications of the observational constraints. | interpretation 0.87 | 0.69 | 0.03 | unclear 0.94 |
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The paper
Original abstract
The brane-world scenario provides an intriguing possibility to explore the phenomenological cosmology implied by string/M theory. In this paper, we consider a modified Randall-Sundrum single brane model with two natural generalizations: a Gauss-Bonnet term in the five-dimensional bulk action as well as an induced gravity term in the four-dimensional brane action, which are the leading-order corrections to the Randall-Sundrum model. We study the influence of these combined effects on the evolution of the primordial gravitational waves generated during an extreme slow-roll inflation on the brane. The background, for the early inflationary era, is then modeled through a de Sitter brane embedded within an anti-de Sitter bulk. In this framework, we show that both effects tend to suppress the Randall-Sundrum enhancement of the amplitude of the tensor perturbations at relatively high energies. Moreover, the Gauss-Bonnet effect, relative to standard general relativity, will abruptly enhance the tensor-to-scalar ratio and break the standard consistency relation at high energies, which cannot be evaded by invoking the induced gravity effect, even though the induced gravity strength would mildly counterbalance these significant changes at high energies. We note that the brane-world model with or without the induced gravity effect fulfills the consistency relation. Finally, we discuss some implications of the observational constraints.
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How the literature uses it
3 arXiv papers cite this in 7 sentences
Papers citing it · 3 sentences without a confident label
Cites it as background 3 papers
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[ref] and the exact solutions of Eq.([ref]) have been analyzed in Refs. [ref] .
Ghosts in the self-accelerating DGP branch with Gauss-Bonnet effect · The model · 0.86
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In the context of GB gravity, several black hole (BH) solutions have been discussed  in the literature [ref] .
Charged spherically symmetric black holes in scalar-tensor Gauss-Bonnet gravity · Introduction · 0.97
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The Gauss-Bonnet effect on the spectra of higher-dimensional GWs was discussed in Refs. [ref] .
Gravitational waves and extra dimensions: a short review · Sources and spectra of gravitational waves · 0.93
What it cites · 30 sentences without a confident label
Uses data or values from 2 papers
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We now discuss the implications of the observational constraints from the Planck mission, which gives a constraint on the power spectrum of the scalar perturbations $P_S$ [ref] (notice that the amplitudes $A^2_S$ and $A^2_T$ are normalized as $A^2_S≡4/25 P_S$ and $A^2_T≡1/100 P_T$, respectively): $P_S=2.215×10^-9$ at the pivot scale $k_*=0.05Mpc^-1$, and an upper bound on the tensor-to-scalar ratio $r$ [ref] : $r≡P_T/P_S≤0.11$ at the pivot scale $k_*=0.002 Mpc^-1$.
Planck 2013 results. XVI. Cosmological parameters · Observational constraints · 1.00
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We now discuss the implications of the observational constraints from the Planck mission, which gives a constraint on the power spectrum of the scalar perturbations $P_S$ [ref] (notice that the amplitudes $A^2_S$ and $A^2_T$ are normalized as $A^2_S≡4/25 P_S$ and $A^2_T≡1/100 P_T$, respectively): $P_S=2.215×10^-9$ at the pivot scale $k_*=0.05Mpc^-1$, and an upper bound on the tensor-to-scalar ratio $r$ [ref] : $r≡P_T/P_S≤0.11$ at the pivot scale $k_*=0.002 Mpc^-1$.
Planck 2013 results. XXII. Constraints on inflation · Observational constraints · 1.00
Compares with 2 papers
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As a result, the combined effect from both GB and IG curvature modifications, in the relatively high-energy inflationary era, gives rise to a suppression effect on the amplitude of the primordial gravitational waves as compared with the one in the original RS2 model (cf. the pure RS2 model [ref] , the modified RS2 model with only a GB effect [ref] and an IG effect alone [ref] ).
Gravitational waves from inflation on the brane · conclusions · 0.98
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A similar behavior has been obtained for the scalar perturbations in the same system [ref] .
Scalar perturbations from brane-world inflation with curvature effects · introduction · 0.80
Cites as support 1 paper
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When stretched to superhorizon scales during the inflation era, the heavy modes, with $m^2>9/4 H^2$, continue to oscillate, but their amplitudes are rapidly and strongly suppressed on large scales and remain in their vacuum state, whose contributions can be neglected later on [ref] .
Gravitational waves from inflation on the brane · Tensor perturbations on the brane · 0.96
Cites as background 3 papers
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Cosmological perturbations in a quasi–de Sitter inflation have been previously studied in the RS2 model [ref] , and in the generalized RS2 model with just the GB effect [ref] or IG effect alone [ref] .
Gravitational waves from inflation on the brane · introduction · 0.88
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The scalar perturbations in this framework have been studied in Ref. [ref] .
Scalar perturbations from brane-world inflation with curvature effects · Primordial gravitational waves · 0.92
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In this scenario, the Standard Model particles are restricted to the brane, while the gravitons are free to propagate into the whole space (see, for example, the review [ref] ).
Brane-World Gravity · introduction · 0.99
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