Randall-Sundrum Case Research Articles

De Sitter thin brane model

We discuss the large mass hierarchy problem in a braneworld model which represents our acceleratively expanding universe. The Randall-Sundrum (RS) model with warped one extra dimension added to flat 4-dimensional space-time cannot describe our expanding universe. Here, we study instead the de Sitter thin brane model. This is described by the same action as that for the RS model, but the 4-dimensional space-time on the branes is $\rm dS_4$. We study the model for both the cases of positive 5-dimensional cosmological constant $\Lambda_5$ and negative one. In the positive $\Lambda_5$ case, the 4-dimensional large hierarchy necessitates a 5-dimensional large hierarchy, and we cannot get a natural explanation. On the other hand, in the negative $\Lambda_5$ case, the large hierarchy is naturally realized in the 5-dimensional theory in the same manner as in the RS model. Moreover, another large hierarchy between the Hubble parameter and the Planck scale is realized by the ${\mathcal O}(10^2)$ hierarchy of the 5-dimensional quantities. Finally, we find that the lightest mass of the massive Kaluza-Klein modes and the intervals of the mass spectrum are of order $10^2\,\rm GeV$, which are the same as in the RS case and do not depend on the value of the Hubble parameter.

Bulk Randall-Sundrum models, electroweak precision tests, and the 125 GeV Higgs

We present upto date electroweak fits of various Randall Sundrum (RS) models. We consider the bulk RS model, deformed RS and the custodial RS models. For the bulk RS case we find the lightest Kaluza Klein (KK) mode of the gauge boson to be $\sim 8$ TeV while for the custodial case it is $\sim 3$ TeV. The deformed model is the least fine tuned of all which can give a good fit for KK masses $< 2$ TeV depending on the choice of the model parameters. We also comment on the fine tuning in each case.

Tensorial perturbations in a brane with induced gravity

We calculate the amplitude of gravitational waves produced by inflation on a de Sitter brane embedded in five-dimensional anti-de Sitter bulk space-time, extending previous calculations in Randall-Sundrum type cosmology to include the effect of induced gravity corrections on the brane. These corrections arise via a term in the brane action that is proportional to the brane Ricci scalar. We find that, as in the Randall-Sundrum case, there is a mass gap between the discrete zero-mode and a continuum of massive bulk modes, which are too heavy to be excited during inflation. We give the normalisation of the zero-mode as a function of the Hubble rate on the brane and are thus able to calculate the high energy correction to the spectrum of gravitational wave (tensor) modes excited on large scales during inflation from initial vacuum fluctuations on small scales.

Gravitational waves from brane-world inflation with induced gravity

We calculate the amplitude of gravitational waves produced by inflation on a de Sitter brane embedded in five-dimensional anti-de Sitter bulk spacetime, extending previous calculations in Randall-Sundrum type cosmology to include the effect of induced gravity corrections on the brane. These corrections arise via a term in the brane action that is proportional to the brane Ricci scalar. We find that, as in the Randall-Sundrum case, there is a mass gap between the discrete zero-mode and a continuum of massive bulk modes, which are too heavy to be excited during inflation. We give the normalization of the zero-mode as a function of the Hubble rate on the brane and are thus able to calculate the high energy correction to the spectrum of gravitational wave (tensor) modes excited on large scales during inflation from initial vacuum fluctuations on small scales. We also calculate the amplitude of density (scalar) perturbations expected due to inflaton fluctuations on the brane, and show that the usual four-dimensional consistency relation for the tensor/scalar ratio remains valid for brane inflation with induced gravity corrections.

Observational constraints on patch inflation in noncommutative spacetime

We study constraints on a number of patch inflationary models in noncommutative spacetime using a compilation of recent high-precision observational data. In particular, the four-dimensional General Relativistic (GR) case, the Randall-Sundrum (RS) and Gauss-Bonnet (GB) braneworld scenarios are investigated by extending previous commutative analyses to the infrared limit of a maximally symmetric realization of the stringy uncertainty principle. The effect of spacetime noncommutativity modifies the standard consistency relation between the tensor spectral index and the tensor-to-scalar ratio. We perform likelihood analyses in terms of inflationary observables using new consistency relations and confront them with large-field inflationary models with potential V \propto \vp^p in two classes of noncommutative scenarios. We find a number of interesting results: (i) the quartic potential (p=4) is rescued from marginal rejection in the class 2 GR case, and (ii) steep inflation driven by an exponential potential (p \to \infty) is allowed in the class 1 RS case. Spacetime noncommutativity can lead to blue-tilted scalar and tensor spectra even for monomial potentials, thus opening up a possibility to explain the loss of power observed in the cosmic microwave background anisotropies. We also explore patch inflation with a Dirac-Born-Infeld tachyon field and explicitly show that the associated likelihood analysis is equivalent to the one in the ordinary scalar field case by using horizon-flow parameters. It turns out that tachyon inflation is compatible with observations in all patch cosmologies even for large p.

Cosmological perturbations from braneworld inflation with a Gauss-Bonnet term

Braneworld inflation is a phenomenology related to string theory that describes high-energy modifications to general relativistic inflation. The observable universe is a brane embedded in 5-dimensional anti de Sitter spacetime. When the 5-dimensional action is Einstein-Hilbert, we have a Randall-Sundrum type braneworld. The amplitude of tensor and scalar perturbations from inflation is strongly increased relative to the standard results, although the ratio of tensor to scalar amplitudes still obeys the standard consistency relation. If a Gauss-Bonnet term is included in the action, as a high-energy correction motivated by string theory, we show that there are important changes to the Randall-Sundrum case. We give an exact analysis of the tensor perturbations. They satisfy the same wave equation and have the same spectrum as in the Randall-Sundrum case, but the Gauss-Bonnet change to the junction conditions leads to a modified amplitude of gravitational waves. The amplitude is no longer monotonically increasing with energy scale, but decreases asymptotically after an initial rise above the standard level. Using an approximation that neglects bulk effects, we show that the amplitude of scalar perturbations has a qualitatively similar behavior to the tensor amplitude. In addition, the tensor to scalar ratio breaks the standard consistency relation.

Observational constraints on braneworld inflation: The effect of a Gauss-Bonnet term

High-energy modifications to general relativity introduce changes to the perturbations generated during inflation, and the latest high-precision cosmological data can be used to place constraints on such modified inflation models. Recently it was shown that Randall-Sundrum-type braneworld inflation leads to tighter constraints on quadratic and quartic potentials than in general relativity. We investigate how this changes with a Gauss-Bonnet correction term, which can be motivated by string theory. Randall-Sundrum models preserve the standard consistency relation between the tensor spectral index and the tensor-to-scalar ratio. The Gauss-Bonnet term breaks this relation, and also modifies the dynamics and perturbation amplitudes at high energies. We find that the Gauss-Bonnet term tends to soften the Randall-Sundrum constraints. The observational compatibility of the quadratic potential is strongly improved. For a broad range of energy scales, the quartic potential is rescued from marginal rejection. Steep inflation driven by an exponential potential is excluded in the Randall-Sundrum case, but the Gauss-Bonnet term leads to marginal compatibility for sufficient e-folds.

Quantum self-consistency ofAdS×Σbrane models

Continuing our previous work, we consider a class of higher dimensional brane models with the topology of ${\mathrm{AdS}}_{{D}_{1}+1}\ifmmode\times\else\texttimes\fi{}\ensuremath{\Sigma},$ where $\ensuremath{\Sigma}$ is a one-parameter compact manifold and two branes of codimension one are located at the orbifold fixed points. We consider a setup where such a solution arises from Einstein-Yang-Mills theory and evaluate the one-loop effective potential induced by gauge fields and by a generic bulk scalar field. We show that this type of brane model resolves the gauge hierarchy between the Planck and electroweak scales through redshift effects due to the warp factor ${a=e}^{\ensuremath{-}\ensuremath{\pi}\mathrm{kr}}.$ The value of a is then fixed by minimizing the effective potential. We find that, as in the Randall-Sundrum case, the gauge field contribution to the effective potential stabilizes the hierarchy without fine-tuning as long as the Laplacian ${\ensuremath{\Delta}}_{\ensuremath{\Sigma}}$ on $\ensuremath{\Sigma}$ has a zero eigenvalue. Scalar fields can stabilize the hierarchy depending on the mass and the nonminimal coupling. We also address the quantum self-consistency of the solution, showing that the classical brane solution is not spoiled by quantum effects.

Moduli effective action in warped brane-world compactifications

We consider a class of 5D brane-world solutions with a power-law warp factor a( y)∝ y q , and bulk dilaton with profile φ∝ln y, where y is the proper distance in the extra dimension. This class includes the heterotic M-theory brane-world of [Phys. Rev. D 59 (1999) 086001, and hep-th/0103239] and the Randall–Sundrum (RS) model as a limiting case. In general, there are two moduli fields y ±, corresponding to the “positions” of two branes (which live at the fixed points of an orbifold compactification). Classically, the moduli are massless, due to a scaling symmetry of the action. However, in the absence of supersymmetry, they develop an effective potential at one loop. Local terms proportional to K ± 4, where K ±= q/ y ± is the local curvature scale at the location of the corresponding brane, are needed in order to remove the divergences in the effective potential. Such terms break the scaling symmetry and hence they may act as stabilizers for the moduli. When the branes are very close to each other, the effective potential induced by massless bulk fields behaves like V∼ d −4, where d is the separation between branes. When the branes are widely separated, the potentials for each one of the moduli generically develop a “Coleman–Weinberg”-type behaviour of the form a 4( y ±) K ± 4ln( K ±/ μ ±), where μ ± are renormalization scales. In the RS case, the bulk geometry is AdS and K ± are equal to a constant, independent of the position of the branes, so these terms do not contribute to the mass of the moduli. However, for generic warp factor, they provide a simple stabilization mechanism. For q≳10, the observed hierarchy can be naturally generated by this potential, giving the lightest modulus a mass of order m −≲TeV.

GRAVITATIONAL HIGGS MECHANISM

We discuss the gravitational Higgs mechanism in domain wall background solutions that arise in the theory of five-dimensional Einstein–Hilbert gravity coupled to a scalar field with a nontrivial potential. The scalar fluctuations in such backgrounds can be completely gauged away, and so can be the graviphoton fluctuations. On the other hand, we show that the graviscalar fluctuations do not have normalizable modes. As to the four-dimensional graviton fluctuations, in the case where the volume of the transverse dimension is finite the massive modes are plane-wave normalizable, while the zero mode is quadratically normalizable. We then discuss the coupling of domain wall gravity to localized four-dimensional matter. In particular, we point out that this coupling is consistent only if the matter is conformal. This is different from the Randall–Sundrum case as there is a discontinuity in the δ-function-like limit of such a smooth domain wall — the latter breaks diffeomorphisms only spontaneously, while the Randall–Sundrum brane breaks diffeomorphisms explicitly. Finally, at the quantum level both the domain wall as well as the Randall–Sundrum setups suffer from inconsistencies in the coupling between gravity and localized matter, as well as the fact that gravity is generically expected to be delocalized in such backgrounds due to higher curvature terms.