De Sitter Brane Research Articles

Localization of scalar field on the brane-world by coupling with gravity

In this paper, we consider a coupling mechanism between the kinetic term and the gravity, in which a coupling function F (R) is introduced into the kinetic term of the five-dimensional scalar field. Based on this scenario, we investigate the localization of scalar fields in three specific braneworld models: the Minkowski brane, the de Sitter brane, and the Anti-de Sitter brane. The brane models considered here are regular with no singularity for scalar curvature. For the Minkowshi brane case, the zero mode can always be localized on the brane, and the massive modes can be localized or quasi-localized on the brane. For the dS4 brane case, two forms of factor F (R) is considered. The zero mode can always be localized, and the massive modes could be quasi-localized on the brane. Besides, with the second coupling factor, the scalar zero mode could be localized on the both sides of the origin of extra dimension, while the massive modes could be quasi-localized on the origin. Lastly, for the AdS4 brane case, the localization of the scalar zero mode requires the consideration of a coupling potential V (Φ, φ), while the massive modes can still be localized on the brane with an infinite number.

Non-trivial thick brane realisations with 3-forms

We explore the construction of four-dimensional thick branes supported by massless 3-forms in a five-dimensional bulk space. The required residual Poincaré symmetry on the brane is realised as a combination of the bulk symmetries and the internal gauge symmetry of the 3-form. We show the presence of a gradient instability for the perturbations orthogonal to the brane when its profile decays slowly in the asymptotic regions. In particular, we ascertain that the prevailing profiles found in the literature are susceptible to such instabilities. We confirm our results by transitioning to the dual formulation in terms of a shift-symmetric scalar. In this formulation, the residual Poincaré group is trivially realised without internal symmetries, and there is a diagonal translational invariance in the fifth dimension reminiscent of the invariance under translations orthogonal to the brane of the dual 3-form. We demonstrate the extension of our results to the cases of de Sitter and Anti de Sitter branes where the gradient instabilities of asymptotically slowly decaying branes persist. Finally, we briefly comment on the construction of thick branes with massive 3-forms and their 1-form duals.

Nested warped geometry in a non-flat braneworld scenario

We generalize nested multiply warped braneworld models by incorporating non-zero brane curvature caused by an effective cosmological constant Omega induced on the 3-branes. Starting with the doubly warped model, we first analyze the case where the maximally warped brane is identified as the visible brane. For Omega <0, resolution of the gauge hierarchy problem imposes a small upper bound on |Omega |, and can possibly lead to positivity of all the 3-brane tensions. For Omega >0, the latter is not possible but the tuning of the cosmological constant to its tiny observed value is linked to the tuning of the extra dimensional moduli close to the inverse Planck length, justifying the original flat brane approximation. In both regimes, we study the dependence of the scale-clustering of the pair of TeV-branes on the brane cosmological constant and hence its potential role in generating a fermion mass hierarchy between these branes. Identifying the near-maximally warped brane as the visible brane instead opens up regions in the parameter space that allow positive 3-brane tensions for both anti de Sitter and de Sitter branes, subject to non-trivial constraints on the warping parameters. We conclude by generalizing the key results to arbitrary n-fold nested warped braneworlds.

Thick brane in Rastall gravity

In this work, thick branes in Rastall gravity are investigated. Three types of maximally symmetric thick brane models are constructed and the linear tensor perturbation is analyzed. In the flat brane model, the tensor modes of the perturbation are either unstable or nonlocalizable for a nonvanishing Rastall parameter. In the de Sitter brane model, only the ground state of the tensor mode is localized. In the anti-de Sitter brane model, the number of the bound tensor states is infinity. For both the de Sitter and anti-de Sitter brane models, the condition of stability for the Rastall parameter is obtained. The linear scalar perturbations are also considered for the three brane models.

Kalb–Ramond field localization on a thick de Sitter brane

In this paper, we explore the localization condition of Kalb–Ramond (KR) tensorial gauge field on a thick de Sitter (dS) brane. Following the localization mechanism in the work by Chumbes et al (2012 Phys. Rev. D 85 085003), we analyze the localization of KR tensorial gauge field on a non-flat three-brane. We propose three kinds of coupling methods and two of them support the localization of zero mode. In addition, there exist resonant Kaluza–Klein modes on the thick dS brane. The effects of three parameters on the localization and the resonant mode for the KR field are also discussed.

Localization of Elko spinor fields in tachyonic de Sitter braneworld models

In this paper, we investigate the localization of a five-dimensional (5D) Elko spinor field in de Sitter tachyonic braneworld models. These branes are generated by gravity coupled to a tachyonic bulk scalar field and include a de Sitter cosmological background induced on the 3D-brane. Using Yukawa-type coupling mechanism we show that a free massless Elko spinor field cannot be localized on tachyonic de Sitter branes while massive Elko fields are localized if their bulk mass obeys an upper bound. Also by introducing a tachyonic function F(T) as Yukawa interaction term between the Elko spinor and the background tachyonic scalar field we find that localized massless zero modes are given in terms of general Heun functions. Furthermore, it is shown that employing a new derivative coupling term in the action of Elko spinor fields leads to the Elko field localization on tachyonic de Sitter branes.

The massive Elko spinor field in the de Sitter braneworld model

The Elko spinor field is a spin 1/2 fermionic quantum field with a mass dimension introduced as a candidate of dark matter. In this work, we study the localization of Elko fields on a de Sitter thick brane constructed by a canonical or phantom scalar field. By presenting the mass-independent potentials of Kaluza-Klein (KK) modes in the corresponding Schrödinger equations, it is shown that the Elko spinor field with a five- dimensional mass term can be localized on de Sitter branes. Also, by using a Yukawa type coupling term, we find that the Elko spinor field can be localized on this brane with a particular coupling constant. Furthermore, it is shown that the zero mode of the Elko field is localized on the de Sitter brane through a Yukawa geometrical coupling term.

De Sitter branes in a flat bulk of massive gravity

We construct de Sitter branes in a flat bulk of massive gravity in 5D. We find two branches of solutions, reminiscent of the normal and self-accelerating branches in DGP, but with rather different properties. Neither branch has a self-accelerating limit: the background geometry requires having a nonvanishing tension. On the other hand, on both branches there are sub-branches where the leading order contributions of the tension to the curvature cancel. In these cases it turns out that larger tensions curve the background less. Further, both branches support a localized 4D massless graviton for a special choice of bulk mass terms. This choice may be protected by enhanced gauge symmetry. Finally, we generalize the solutions to the case of bigravity in a flat 5D bulk.

Localization of massless Elko spinor fields on de Sitter thick branes

In this work, we investigate the localization of a five-dimensional (5D) free massless Elko spinor field on de Sitter thick branes that are generated by a canonical or phantom scalar field. It is shown that the zero mode of Elko field cannot be localized on the de Sitter brane. In order to circumvent this problem, we employ a nonminimal coupling term in the 5D Elko spinor field action and find that the Elko field can be localized on the de Sitter brane with this mechanism.

Constant curvature black holes in Einstein AdS gravity: Euclidean action and thermodynamics

We compute the Euclidean action for constant curvature black holes (CCBHs), as an attempt to associate thermodynamic quantities to these solutions of Einstein anti-de Sitter (AdS) gravity. CCBHs are gravitational configurations obtained by identifications along isometries of a $D$-dimensional globally AdS space, such that the Riemann tensor remains constant. Here, these solutions are interpreted as extended objects, which contain a $(D-2)$-dimensional de-Sitter brane as a subspace. Nevertheless, the computation of the free energy for these solutions shows that they do not obey standard thermodynamic relations.

Hydrogen-like spectrum of spontaneously created brane universes with de-Sitter ground state

Unification of Randall–Sundrum and Regge–Teitelboim brane cosmologies gives birth to a serendipitous Higgs–deSitter interplay. A localized Dvali–Gabadadze–Porrati scalar field, governed by a particular (analytically derived) double-well quartic potential, becomes a mandatory ingredient for supporting a deSitter brane universe. When upgraded to a general Higgs potential, the brane surface tension gets quantized, resembling a Hydrogen atom spectrum, with deSitter universe serving as the ground state. This reflects the local/global structure of the Euclidean manifold: From finite energy density no-boundary initial conditions, via a novel acceleration divide filter, to exact matching conditions at the exclusive nucleation point. Imaginary time periodicity comes as a bonus, with the associated Hawking temperature vanishing at the continuum limit. Upon spontaneous creation, while a finite number of levels describe universes dominated by a residual dark energy combined with damped matter oscillations, an infinite tower of excited levels undergo a Big Crunch.

Wave fluctuations near a de Sitter brane in an anti-de Sitter universe

We investigate the Klein–Gordon equation in the past causal domain of a de Sitter brane imbedded in an anti-de Sitter bulk. We solve the global mixed hyperbolic problem. We prove that any finite energy solution can be expressed as a Kaluza–Klein tower that is a superposition of free fields in the Steady State Universe, of which we study the asymptotic behaviors. We show that the leading term of a gravitational fluctuation is a massless graviton, i.e. the de Sitter brane is linearly stable.

Localization and mass spectra of bulk bosonic fields on de Sitter thick branes

A thick de Sitter brane constructed by a canonical or phantom scalar field and localization mass spectra of the bulk scalar and vector fields on the de Sitter brane is investigated. It is found that the scalar and vector zero modes are always localized on the de Sitter brane. For the de Sitter brane generated by a canonical scalar field, the spectrum of the scalar (vector) KK modes consists of one or two bound modes (one bound mode) and a set of continuous modes. However, for the de Sitter brane generated by a phantom scalar field, the spectrum of the scalar (vector) KK modes consists of two (one) or more bound KK modes as well as a set of continuous modes. The continuous spectrum on both branes starts with a same value for the scalar (vector) KK modes.

On the Klein–Gordon equation near a de Sitter brane

In this paper we investigate the Klein–Gordon equation in the past causal domain of a de Sitter brane imbedded in an Anti-de Sitter bulk. We solve the global mixed hyperbolic problem. We prove that any finite energy solution can be expressed as a Kaluza–Klein tower that is a superposition of free fields in the Steady State Universe, of which we study the asymptotic behaviours. We show that the leading term of a gravitational fluctuation is a massless graviton, i.e. the de Sitter brane is linearly stable. Beyond the Cauchy horizon, the energy of the waves can tend to infinity at the moment the brane hits the conformal time-like boundary.

Ghosts in the self-accelerating DGP branch with Gauss–Bonnet effect

The Dvali-Gabadadze-Porrati brane-world model provides a possible approach to address the late-time cosmic acceleration. However, it has subsequently been pointed out that a ghost instability will arise on the self-accelerating branch. Here, we carefully investigate whether this ghost problem could be possibly cured by introducing the Gauss-Bonnet term in the five-dimensional bulk action, a natural generalization to the Dvali-Gabadadze-Porrati model. Our analysis is carried out for a background where a de Sitter brane is embedded in an anti-de Sitter bulk. Our result shows that the ghost excitations cannot be avoided even in this modified model.

Mapping AdS to dS spaces and back

We derive a map between Einstein spaces of positive and negative curvature, including scalar matter. Starting from a space of positive curvature with some dimensions compactified on a sphere and analytically continuing the number of compact dimensions, we obtain a space of negative curvature with a compact hyperbolic subspace, and vice versa. Prime examples of such spaces are de Sitter (dS) and anti--de Sitter (AdS) space, as well as black hole spacetimes with (A)dS asymptotics and perturbed versions thereof, which play an important role in holography. This map extends work done by Caldarelli et al., who map asymptotically AdS spaces to Ricci-flat ones. A remarkable result is that the boundary of asymptotically AdS spaces is mapped to a brane in the bulk of de Sitter, and perturbations near the AdS boundary are sourced by a stress tensor confined to this brane. We also calculate the Brown-York stress tensor for the perturbed AdS metric, which turns out to be the negative of the stress tensor on the de Sitter brane. The map can also be used as a solution generator, and we obtain a Kerr/AdS solution with hyperbolic horizon from a known Kerr/dS one.

Quantum effects in topological and Schwarzschild de Sitter brane: Aspects of torsion on $(D\!{\bar D})_4$-brane

We investigate an effective torsion curvature in a second-order formalism underlying a two-form world-volume dynamics in a D5-brane. In particular, we consider the two form in presence of a background (open string) metric in a U(1) gauge theory. Interestingly the formalism may be viewed via a noncoincident pair of [Formula: see text]-brane with a global Nereu–Schwarz (NS) two form on an anti-brane and a local two form on a brane. The energy–momentum tensor is computed in the six-dimensional (6D) conformal field theory (CFT). It is shown to source a metric fluctuation on a vacuum created pair of [Formula: see text]-brane at a cosmological horizon by the two-form quanta in the gauge theory. The emergent gravity scenario is shown to describe a low-energy (perturbative) string vacuum in 6D with a nonperturbative (NP) quantum correction by a lower (p &lt; 5) dimensional Dp-brane or an anti-brane in the formalism. A closed string exchange between a pair of [Formula: see text]-brane, underlying a closed/open string duality, is argued to describe the Einstein vacuum in a low-energy limit. We obtain topological de Sitter (TdS) and Schwarzschild brane universe in six dimensions. The brane/anti-brane geometries are analyzed to explore some of their characteristic and thermal behaviors in presence of the quantum effects. They reveal an underlying nine-dimensional type IIA and IIB superstring theories on S1.

Matter Confinement Mechanism in de Sitter Brane

The geodesic equation in induced matter theory with de Sitter brane is described. It is shown that the extra forces do not change the four-impulse of massive particles. We also show that the variation of length of the 4-velocity of a test particle in de Sitter brane along the extra dimensions could remain finite resulting in a fluctuating component and hence keeping the particle inside the 4D spacetime and within the observable physics. In fact, the extra components trace closed orbits keep them finite in length. All of these are formulated in the framework of a dynamical system and we characterize the behaviour of the integral curves of this system.

An Exact Class of Bulk Field Potentials onto the 5D-Warp of de Sitter Spacetime

In the five-dimensionally warped FRW Universe, we integrate the corresponding Einstein equations for a scalar source depending only on the extra-dimension. It yields a de Sitter brane and a specific warp factor for which we derive the effective bulk field potentials. These are generalizing some of the previously proposed forms in the literature.

Braneworlds with field derivative coupling to the Einstein tensor

In this paper, we investigate the Randall-Sundrum type braneworld models in the scalar-tensor theory with field derivative coupling to the Einstein tensor. We first formulate the generalized junction conditions of the metric and the scalar field on the timelike codimension-one hypersurface (=brane). With the use of these junction conditions, we then derive the Minkowski and de Sitter brane solutions embedded into the $Z_2$-symmetric five-dimensional anti-de Sitter (AdS) bulk spacetime. The configuration of the scalar field depends on the slice of the AdS spacetime. These branes are supported by the tension and not coupled to the scalar field. The Minkowski brane solution can be obtained when the brane tension is tuned to the bulk contributions. Once this tuning relation is broken, the de Sitter brane solutions are obtained. The de Sitter brane solutions have two branches. One has the smooth limit to the case where the scalar field becomes trivial, while the other branch does not. The latter branch has the upper bound on the brane tension, where the expansion rate vanishes. Finally, we investigate the low energy effective gravitational theory realized on the brane, which is given by the four-dimensional Einstein-scalar theory with the corrections from the bulk. In the case that there is no generation of the dark radiation from the bulk scalar field, we recover the the four-dimensional Einstein-scalar theory.