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On gravity localization in scalar braneworlds with a super-exponential warp factor
High Energy Physics - Theory · Submitted 1 Oct 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that within tachyonic braneworld models,"super-exponential" warp factors of the form $e^{-2f} \sim e^{-2c_1e^{c_2 |\sigma|}}$ are problematic when dealing with both the finiteness of the effective four-dimensional (4d) Planck mass and the localization of 4d gravity, which can be stated by the requirement that $\int e^{-2f(\sigma)}d\sigma < \infty$, because this condition necessarily implies that c_1 and c_2 should be positive.
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The abstract, sentence by sentence
We show that within tachyonic braneworld models,"super-exponential" warp factors of the form $e^{-2f} \sim e^{-2c_1e^{c_2 |\sigma|}}$ are problematic when dealing with both the finiteness of the effective four-dimensional (4d) Planck mass and the localization of 4d gravity, which can be stated by the requirement that $\int e^{-2f(\sigma)}d\sigma < \infty$, because this condition necessarily implies that c_1 and c_2 should be positive. As a consequence of this fact the tachyonic field $T$ turns out to be complex in contradiction with the real nature of the starting action for the tachyonic braneworld. Conversely if one requires to have a real tachyon field, 4d gravity will not be localized and the effective gravitational coupling will be infinite. We present several typical examples where this problem occurs: we have analysed this situation for thin as well as thick tachyonic braneworlds with 4d Poincare symmetry, for the case when a bulk cosmological constant is present, and even for a brane with an induced spatially flat 4d cosmological background, and shown that in all cases the tachyon field T comes out to be inconsistently complex when imposing localization of 4d gravity. On the other hand, when dealing with a further reduction of the hierarchy problem one should carefully consider the sign of the constants c_1 and c_2 to avoid inconsistencies in the tachyonic braneworld model. We also present a similar discusion involving a canonical scalar field in the bulk where none of these problems arise and hence, the mass hierarchy and 4d gravity localization problems can be successfully addressed at once. Finally, the stability analysis of this scalar tensor braneworld model with a super-exponential warp factor is performed.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We show that within tachyonic braneworld models,"super-exponential" warp factors of the form $e^{-2f} \sim e^{-2c_1e^{c_2 |\sigma|}}$ are problematic when dealing with both the finiteness of the effective four-dimensional (4d) Planck mass and the localization of 4d gravity, which can be stated by the requirement that $\int e^{-2f(\sigma)}d\sigma < \infty$, because this condition necessarily implies that c_1 and c_2 should be positive. | result 0.87 | 0.87 | 0.47 | asserted 1.00 |
| s1 | As a consequence of this fact the tachyonic field $T$ turns out to be complex in contradiction with the real nature of the starting action for the tachyonic braneworld. | result 0.84 | 0.90 | 0.24 | asserted 1.00 |
| s2 | Conversely if one requires to have a real tachyon field, 4d gravity will not be localized and the effective gravitational coupling will be infinite. | result 0.93 | 0.83 | 0.31 | asserted 1.00 |
| s3 | We present several typical examples where this problem occurs: we have analysed this situation for thin as well as thick tachyonic braneworlds with 4d Poincare symmetry, for the case when a bulk cosmological constant is present, and even for a brane with an induced spatially flat 4d cosmological background, and shown that in all cases the tachyon field T comes out to be inconsistently complex when imposing localization of 4d gravity. | contribution 0.72 | 0.95 | 0.23 | asserted 1.00 |
| s4 | On the other hand, when dealing with a further reduction of the hierarchy problem one should carefully consider the sign of the constants c_1 and c_2 to avoid inconsistencies in the tachyonic braneworld model. | interpretation 0.83 | 0.37 | 0.14 | hedged possibility 0.61 |
| s5 | We also present a similar discusion involving a canonical scalar field in the bulk where none of these problems arise and hence, the mass hierarchy and 4d gravity localization problems can be successfully addressed at once. | contribution 0.60 | 0.89 | 0.17 | asserted 0.99 |
| s6 | Finally, the stability analysis of this scalar tensor braneworld model with a super-exponential warp factor is performed. | contribution 0.94 | 0.93 | 0.06 | asserted 0.94 |
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The paper
Original abstract
We show that within tachyonic braneworld models,"super-exponential" warp factors of the form $e^{-2f} \sim e^{-2c_1e^{c_2 |\sigma|}}$ are problematic when dealing with both the finiteness of the effective four-dimensional (4d) Planck mass and the localization of 4d gravity, which can be stated by the requirement that $\int e^{-2f(\sigma)}d\sigma < \infty$, because this condition necessarily implies that c_1 and c_2 should be positive. As a consequence of this fact the tachyonic field $T$ turns out to be complex in contradiction with the real nature of the starting action for the tachyonic braneworld. Conversely if one requires to have a real tachyon field, 4d gravity will not be localized and the effective gravitational coupling will be infinite. We present several typical examples where this problem occurs: we have analysed this situation for thin as well as thick tachyonic braneworlds with 4d Poincare symmetry, for the case when a bulk cosmological constant is present, and even for a brane with an induced spatially flat 4d cosmological background, and shown that in all cases the tachyon field T comes out to be inconsistently complex when imposing localization of 4d gravity. On the other hand, when dealing with a further reduction of the hierarchy problem one should carefully consider the sign of the constants c_1 and c_2 to avoid inconsistencies in the tachyonic braneworld model. We also present a similar discusion involving a canonical scalar field in the bulk where none of these problems arise and hence, the mass hierarchy and 4d gravity localization problems can be successfully addressed at once. Finally, the stability analysis of this scalar tensor braneworld model with a super-exponential warp factor is performed.
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How the literature uses it
4 arXiv papers cite this in 12 sentences
Papers citing it · 9 sentences without a confident label
Compares with it 1 paper
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Thus, we have found a new scalar field configuration for which both the 4D gravity localization and the gauge hierarchy problems can be tackled with the same kind of warp factors, contrary to previous results where the scalar field usually turns out to be complex when attempting to localize 4D gravity in the $3$–brane (see, for instance, [ref] – [ref] ).
Discrete graviton spectrum from super-exponential cup potentials and their application to braneworld physics · Summary of results and discussion · 0.95
Cites it as background 2 papers
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In fact, thick brane cosmology has been widely discussed in [ref] , further regarding other type of warp factors [ref] and tachyonic solutions, with a decaying warp factor that enables localization of 4D gravity as well as other matter fields [ref] .
Spherically Symmetric Thick Branes Cosmological Evolution · Introduction · 0.97
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Different kinds of scalar field configurations coupled to gravity in distinct ways, yield different physical scenarios as it can be seen in e.g. [ref] – [ref] .
Discrete graviton spectrum from super-exponential cup potentials and their application to braneworld physics · Introduction · 0.98
What it cites · 4 sentences without a confident label
Uses the method or tool of 1 paper
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We shall analyze the localization of 4d gravity in our braneworld field configuration following the work presented in [ref] , where a generalization of the Bardeen formalism for metric fluctuations of higher–dimensional backgrounds with non–compact extra dimensions was accomplished (see also [ref] and [ref] for similar approaches); moreover, the master equations for the coupled system of metric and scalar perturbations were also derived in a gauge–invariant form.
Stability of Scalar Fields in Warped Extra Dimensions · Tensor perturbations and localization of 4d gravity · 0.99
Cites as background 3 papers
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Several authors have chosen a tachyonic scalar field in the bulk and address issues like the hierarchy problem, and localization of gravity and matter fields [ref] – [ref] .
A de Sitter tachyon thick braneworld · Introduction · 0.97
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It has also become a matter of interest to find smooth braneworld solutions (for interesting reviews on these issues see e.g., [ref] – [ref] ).
Thick brane solutions · Introduction · 1.00
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It has also become a matter of interest to find smooth braneworld solutions (for interesting reviews on these issues see e.g., [ref] – [ref] ).
Brane-World Gravity · Introduction · 1.00
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