Thick Brane Research Articles

Evolution of fermion resonance in thick brane

Abstract In this work, we investigate the numerical evolution of massive Kaluza–Klein (KK) modes of a Dirac field on a thick brane. We deduce the Dirac equation in five-dimensional spacetime, and obtain the time-dependent evolution equation and Schrödinger-like equation of the extra-dimensional component. We use the Dirac KK resonances as the initial data and study the corresponding dynamics. By monitoring the decay law of the left- and right-chiral KK resonances, we compute the corresponding lifetimes and find that there could exist long-lived KK modes on the brane. Especially, for the lightest KK resonance with a large coupling parameter and a large three momentum, it will have an extremely long lifetime.

Quasibound and quasinormal modes of a thick brane in Rastall gravity

In this work, we study the gravitational quasinormal modes of the thick brane in Rastall gravity. Using the asymptotic iteration and direct integration methods, we solve the quasinormal frequencies of the Rastall thick brane. We also obtained the waveforms of these quasinormal modes through numerical evolution. The results indicate that although the Rastall thick brane lacks a bound zero mode, when the Rastall parameter λ ≳ 0, a long-lived quasinormal mode appears. This long-lived quasinormal mode may restore the four-dimensional effective Newtonian potential on the brane on a large scale. This may provide a new perspective for the localization of gravity on thick branes, that a thick brane does not necessarily require the gravity to be localized, perhaps quasi-localized is sufficient.

Constraints on extra dimensions theories from gravitational quantum barrier experiments

Abstract We discuss the quantum-bouncer experiment involving ultracold neutrons in a braneworld scenario. Extra-dimensional theories typically predict the strengthening of gravitational interactions over short distances. In this paper, we specifically study the anomalous gravitational interaction between the bouncing neutron and the reflecting mirror, resulting from hidden dimensions, and investigate the effects of this new interaction on the outcome of the quantum-bouncer experiment in the context of a thick brane model. This analysis allows us to identify which physical quantity of the extra-dimensional theory this neutron experiment is capable of constraining. Based on the experimental data, we found a new and independent empirical bound on the free parameters of the model: the higher-dimensional gravitational constant and a parameter related to a transverse width of the confined matter inside the thickbrane. This new bound is valid in scenarios with an arbitrary number of extra dimensions greater than two. In this manner, by considering the thickness of the brane, we have been able to extend previous studies on this topic, which were limited to models with few codimensions, due to non-computability problems of power-law corrections of the gravitational potential.

The dynamics of three-forms in thick branes

In this work, we investigate thick brane models with a single three-form field. We find novel solutions for thick braneworlds where only three-forms exist and interact gravitationally in the bulk, both with and without matter fields. We use an additional scalar field as proxy for the matter fields. As an initial study, we consider the results here in contrast to the single scalar field thick braneworld case. The properties of the specific three-form parameterisation limits the freedom we have to choose the form of the warp factor, leading to a closed system of equations with nontrivial yet unstable solutions. The stability of the gravitational sector for thick brane three-forms is investigated and the models are shown to be unstable against small perturbations of the metric, further indicating that three-forms cannot exist stably in thick braneworld settings.

Braneworlds in warped Einsteinian cubic gravity

Einstenian cubic gravity (ECG) is a modified theory of gravity constructed with cubic contractions of the curvature tensor. This theory has the remarkable feature of having the same two propagating degrees of freedom of Einstein gravity (EG), at the perturbative level on maximally symmetric spacetimes. The additional unstable modes steaming from the higher order derivative dynamics are suppressed provided that we consider the ECG as an effective field theory wherein the cubic terms are seen as perturbative corrections of the Einstein-Hilbert term. Extensions of ECG have been proposed in cosmology and compact objects in order to probe if this property holds in more general configurations. In this work, we construct a modified ECG gravity in a five dimensional warped braneworld scenario. By assuming a specific combination of the cubic parameters, we obtained modified gravity equations of motion with terms up to second-order. For a thin 3-brane, the cubic-gravity corrections yield an effective positive bulk cosmological constant. Thus, in order to keep the 5D bulk warped compact, an upper bound of the cubic parameter with respect to the bulk curvature was imposed. For a thick brane, the cubic-gravity terms modify the scalar field potential and its corresponding vacuum. Nonetheless, the domain-wall structure with a localized source is preserved. At the perturbative level, the Kaluza-Klein (KK) tensor gravitational modes are stable and possess a localized massless mode provided the cubic corrections are small compared to the EG braneworld.

Localization of scalar matter with nonminimal derivative coupling on braneworlds

The localization of scalar matter with nonminimal derivative coupling (NMDC) in the braneworld model is studied. Two types of brane models are considered: a thin brane (the Modified Randall-Sundrum) and a thick brane generated by the bulk scalar field. The 5-dimensional theory of scalar field with NMDC is reduced to the effective 4-dimensional theory by imposing the fulfillment of localization conditions. In this article, the localization properties of field with NMDC are examined in both models. We found that the massless and massive scalar field with NMDC can be localized on the MRS thin brane. In the thick brane, the massless scalar field is localized.

Thick Branes in Horndeski Gravity

We investigate thick brane solutions in the Horndeski gravity. In this setup, we found analytical solutions, applying the first-order formalism to two scalar fields where the first field comes from the nonminimal scalar-tensor coupling and the second is due to the matter contribution sector. With these analytical solutions, we evaluate the symmetric thick brane solutions in Horndeski gravity with four-dimensional geometry. In such a setup, we evaluate the gravity fluctuations to find “almost massless modes,” for any values of the Horndeski parameters. These modes were used to compute the corrections to the Newtonian potential and evaluate the limit four-dimensional gravity.

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.

Characteristic modes of a thick brane: Resonances and quasinormal modes

Characteristic modes of a thick brane: Resonances and quasinormal modes

Flat and bent branes in Born–Infeld-like scalar field models

In this work, we investigate the presence of thick branes modeled by a single scalar field with Born–Infeld-like dynamics. We consider the 4-dimensional metric being Minkowski, de Sitter or anti-de Sitter. We obtain the field equations and the conditions to get a first order formalism compatible with them. To illustrate our procedure, some specific models are presented. They support localized warp factor and have their properties controlled by the 4-dimensional cosmological constant. In particular, a hybrid brane may arise, with a thick or thin profile depending on the extra dimension being inside or outside a compact space.

Localization of gravitino field with non-minimal coupling on a thick brane

In this paper, we investigate localization of a five-dimensional gravitino field on a thick brane with non-minimal coupling. By choosing the gauge condition Ψ z = 0, the equations of the Kaluza-Klein (KK) modes of gravitino are obtained. Compared with the case without non-minimal coupling,considering non-minimal coupling can make the zero mode and massive KK modes of a five-dimensional free massless gravitino field be localized on the brane. By considering the Yukawa-like coupling and the non-minimum coupling simultaneously, it is found that the non-minimal coupling will change the mass spectrum of the KK modes and provide more possibility to localize KK modes.

Thick branes via higher order field theory models with exponential and power-law tails

In this work, we obtain exact thick brane models in 4+1 dimensions generated by higher order field theory kinks, inspired by specific potentials for phi ^{10} and phi ^{18} models. We verify that the geodesic equation along the fifth dimension confirms the confining effects of the scalar field on the brane for all of these models. These models provide new solutions with exponential and power-law tails which live in different topological sectors. We show that the resulting branes of specific exponential law models do not possess Z_2-symmetry. Furthermore, we examine the stability of the thick branes, by determining the sign of the w^2 term in the expansion of the potential for the resulting Schrödinger-like equation. It turns out that two of the three models of the phi ^{10} brane are stable, while another contains unstable modes for certain ranges of the model parameters. We also show that the brane solution from the specific phi ^{18} models are stable, while the others involve neutral equilibrium. The asymptotic behaviour of the brane solutions are also discussed.

Energy Transport for Thick Holographic Branes.

Universal properties of two-dimensional conformal interfaces are encoded by the flux of energy transmitted and reflected during a scattering process. We develop an innovative method that allows us to use results for the energy transmission in thin-brane holographic models to find the energy transmission for general smooth domain-wall solutions of three-dimensional gravity. Our method is based on treating the continuous geometry as a discrete set of branes. As an application, we compute the transmission coefficient of a Janus interface in terms of its deformation parameter.

Localization of abelian gauge fields with Stueckelberg-like geometrical coupling on f(T, B)-thick brane

In the context of f(T, B) modified teleparallel gravity, we investigate the influence of torsion scalar T and boundary term B on the confinement of both the gauge vector and Kalb–Ramond fields. Both fields require a suitable coupling in five-dimensional braneworld scenarios to yield a normalizable zero mode. We propose a Stueckelberg-like geometrical coupling that non-minimally couples the fields to the torsion scalar and boundary term. To set up our braneworld models, we use the first-order formalism in which two kinds of superpotential are taken: sine-Gordon and phi ^{4}-deformed. The geometrical coupling is used to produce a localized zero mode. Moreover, we analyze the massive spectrum for both fields and obtain possible resonant massive modes. Furthermore, we do not find tachyonic modes leading to a consistent thick brane.

Gravity and matter on a pure geometric thick polynomial f(R) brane

In this paper, the solutions of the pure geometric thick $f(R)$ brane are investigated. The formulation of $f(R)$ is chosen as $f(R)=\sum_{i=1}^{n}a_{i}R^{i}+\Lambda$. For the certain value of $n$, the brane solution can be calculated, and when $n=3$, $n=4$, and $n=10$, the thick brane solutions are presented. The solutions is stable under linear tensor fluctuation. The zero mode of gravity and scalar field can be localized on thick $f(R)$ branes naturally. The zero mode of vector field and left-chiral fermion can be localized on thick $f(R)$ branes by introducing the coupling with scalar curvature $R$ of spacetime, and the massive resonant modes can be quasilocalized on the brane with the large coupling coefficients.

Flat and bent branes with inner structure in two-field mimetic gravity

Abstract Inspired by the work Zhong et al. (2018), we study the linear tensor perturbation of both the flat and bent thick branes with inner structure in two-field mimetic gravity. The master equations for the linear tensor perturbations are derived by taking the transverse and traceless gauges. For the Minkowski and Anti-de-Sitter brane, the brane systems are stable against the tensor perturbation. The effective potentials of the tensor perturbations of both the flat and bent thick branes are volcano-like, and this structure may potentially lead to the zero-mode and the resonant modes of the tensor perturbation. We further illustrate the results of massive resonant modes.

The physics of intersecting thick to thin branes

We model four-dimensional junctions made out of intersections of co-dimension one brane living in higher-dimensional spacetimes through domain walls. We take a new look at the problem of localizing fermion states on brane junctions as a result of intersecting one thick brane to others sufficiently thin. All the branes intersect orthogonally to form a four-dimensional junction embedded in a higher-dimensional bulk. We discuss the effects of the Yukawa coupling and the proton decay on the restriction of the parameters that control the junction stability and the brane thickness which also define the bulk cosmological constant.

Effective action of a self-interacting scalar field on brane

In extra dimensional theories, the four-dimensional field theory is reduced from a fundamental field theory in the bulk spacetime by integrating the extra dimensional part. In this paper we investigate the effective action of a self-interacting scalar field on a brane in the five-dimensional thick braneworld scenario. We consider two typical thick brane solutions and obtain the Pöschl–Teller and harmonic potentials of the Kaluza–Klein (KK) modes, respectively. The analytical mass spectra and wave functions along extra dimension of the KK modes are obtained. Further, the effective coupling constant between different KK particles, cross section, and decay rate for some processes of the KK particles are related to the fundamental coupling in five dimensions and the new physics energy scale. Some interesting properties of these interactions are found with these calculations. The KK particles with higher mode have longer lifetime, and they almost do not interact with ordinary matter on the brane if their mode numbers are large enough. Thus, these KK particles with higher modes might be a candidate of dark matter.

Evolution of scalar field resonances in a braneworld

In this work, we investigate the numerical evolution of massive Kaluza–Klein (KK) modes of a scalar field in a thick brane. We derive the Klein–Gordon equation in five-dimensional spacetime, and obtain the evolution equation and the Schrödinger-like equation. With the resonances of the scalar KK modes as the initial data, the scalar field is evolved with the maximally dissipative boundary condition. The results show that there are scalar KK resonant particles with long life on the brane, which indicates that these resonances might be regarded as a candidate for dark matter.

Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario

This paper is aimed at investigating the behavior of gauge vector and tensor fields on thick brane in f(T) gravity. This thick brane is not capable of providing a normalizable zero mode for both gauge and Kalb Ramond fields. To overcome this problem, we propose two distinct types of gauge-invariant couplings. In the first coupling, the fields are minimally coupled to the scalar field responsible for generating the thick brane. In the second coupling, we use the geometric coupling in which the fields are non-minimally coupled to torsion. Another issue that we investigate is resonant modes, which allow us to understand the massive spectrum of fields. Indeed we note that an internal structure appears for the Kalb–Ramond massive solutions and both couplings show resonant modes of the massive spectrum.