Thick Brane Solutions Research Articles

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.

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.

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.

Thick branes with inner structure in mimetic f(R) gravity

In this paper, we study the structure and gravitational resonances of thick branes generated by a mimetic scalar field in f(R) gravity. We obtain several typical thick brane solutions for f(R)=R+alpha R^2. To study their stability, we analyze the tensor perturbation of the metric. It is shown that any thick brane model with df/dR>0 is stable and the graviton zero mode can be localized on the brane for each solution, which indicates that the four-dimensional Newtonian gravity can be restored. The effect of the parameter alpha on the gravitational resonances is studied. As a brane splits into multi sub-branes, the effective potential of the tensor perturbation will have an abundant inner structure with multi-wells, and this will lead to new phenomena of the gravitational resonances.

First-Order Formalism and Thick Branes in Mimetic Gravity

In this paper, we investigate thick branes generated by a scalar field in mimetic gravity theory, which is inspired by considering the conformal symmetry under the conformal transformation of an auxiliary metric. By introducing two auxiliary super-potentials, we transform the second-order field equations of the system into a set of first-order equations. With this first-order formalism, several types of analytical thick brane solutions are obtained. Then, tensor and scalar perturbations are analyzed. We find that both kinds of perturbations are stable. The effective potentials for the tensor and scalar perturbations are dual to each other. The tensor zero mode can be localized on the brane while the scalar zero mode cannot. Thus, the four-dimensional Newtonian potential can be recovered on the brane.

Novel modified gravity braneworld configurations with a Lagrange multiplier

In this work we deal with thick brane solutions in the warped five-dimensional braneworld scenario with a single extra spatial dimension of infinite extent, for a class of modified theories of gravity with a Lagrange multiplier. We first present the action, describe the gravity and field equations, outline a strategy to find explicit solutions and explore the stability of the gravitational sector. The investigation deals mainly with the construction of a first order framework capable of using a single scalar field to simulate warp functions that appear in two-field models. In particular, we find specific symmetric and asymmetric brane configurations that engender asymptotic profiles with symmetric and asymmetric five-dimensional anti-de Sitter geometries. Thus, including a Lagrange multiplier unveils an alternative approach to induce brane structure using a single scalar field, tracing out new avenues of research in braneworld scenarios, naturally leading to interesting results for the localization of matter fields in the brane.

Novel thick brane solutions with U(1) symmetry breaking

In this work, using two scalar fields (phi , psi ) coupled to 4 + 1 dimensional gravity, we construct novel topological brane solutions through an explicit U(1) symmetry breaking term. The potential of this model is constructed so that two distinct degenerate vacua in the phi field exist, in analogy to the phi ^{4} potential. Therefore, brane solutions appear due to the vacuum structure of the phi field. However, the topology and vacuum structure in the psi direction depends on the symmetry breaking parameter beta ^{2}, which leads to different types of branes. As a result, one can interpret the present model as a combination of a phi ^{4} brane with an auxiliary field, which leads to deviations from the phi ^{4} system with the brane achieving a richer internal structure. Furthermore, we analyse in detail the behaviour of the superpotentials, the warp factors, the Ricci and Kretschmann scalars and the Einstein tensor components. In addition to this, we explore the stability of the brane in terms of the free parameters of the model. The analysis presented here complements previous work and is sufficiently novel to be interesting.

Z2 -symmetric thick brane with a specific warp function

In this work, we investigate a new warped five-dimensional, ${Z}_{2}$-symmetric thick brane solution in the presence of a real scalar field. We examine the different geometric aspects of the model. We discuss the stability of the solution under gravitational fluctuations and study both the graviton ground state and the continuum of Kaluza-Klein modes to find a correction to Newton's law. Then, we study the quantum version of the model by deriving the Wheeler-DeWitt equation and looking for the corresponding solution. Finally, the cosmology of the brane is studied.

Tensor perturbations and thick branes in higher-dimensional f(R) gravity

We study brane worlds in an anisotropic higher-dimensional spacetime within the context of f(R) gravity. Firstly, we demonstrate that this spacetime with a concrete metric ansatz is stable against linear tensor perturbations under certain conditions. Moreover, the Kaluza-Klein modes of the graviton are analyzed. Secondly, we investigate thick brane solutions in six dimensions and their properties. We further exhibit two sets of solutions for thick branes. At last, the effective potential of the Kaluza-Klein modes of the graviton is discussed for the two solved f(R) models in higher dimensions.

New results on asymmetric thick branes

This work deals with the presence and stability of thick brane solutions in the warped five dimensional braneworld scenario with a single extra spatial dimension of infinite extent. We combine two distinct procedures that give rise to new possibilities, allowing that we describe models of asymmetric thick branes, with the asymmetry being controlled by a single real parameter. We illustrate the main results with some distinct models, which show that the method works for both standard and generalized models, and the solutions are gravitationally stable against small perturbations of the metric.

Linear stability of f(R, \u03d5, X) thick branes: tensor perturbations

We explore thick branes in f (R, ϕ, X) gravity. We obtain the linear tensor perturbation equation of f (R, ϕ, X) branes and show that the branes are stable against the tensor perturbations under the condition of frac{partial fleft(R,phi, Xright)}{partial R}>0 . In order to obtain thick brane solutions of the fourth-order field equations in this theory, we employ the reconstruction technique. We get exact solutions of the specific f (R, ϕ, X) thick brane generated by a noncanonical scalar field. It is shown that the zero mode of the graviton for the thick brane is localized under certain conditions. This implies that the four-dimensional Newtonian potential is recovered on the brane. The effects of the Kaluza-Klein modes of the graviton for the f (R, ϕ, X) thick brane are also discussed.

Frame-invariant approach to higher-dimensional scalar-tensor gravity

The recent interest in modified theories of gravity, involving some type of non-minimal coupling to the Ricci scalar, and the calculation of cosmological observables in the Einstein or the Jordan frame, motivate the formulation of these theories in terms of quantities that are invariant under frame transformations. Furthermore, in view of the description of gravity and its geometry motivated by string theory, such a formulation could be extended to include theories of extra spatial dimensions. In the present article, we generalize the construction of frame-invariant quantities, concerning a general, $D$-dimensional scalar-tensor theory. Then, we limit our scope to the 5D braneworld scenario, where we study thick brane solutions that are localized on the 3-brane and extend the invariant formulation to the case of multiple scalar fields (non-)minimally coupled to gravity.

Braneworld Scenarios from Deformed Defect Chains

Novel braneworld scenarios supported by warp factors driven by a single extra dimension are obtained from deformed one-dimensional lump-like solutions known {\em a priori}. Through a novel {\em ansatz}, the internal energy structure, the braneworld warp factor, and the quantum mechanical analogue problem, as well as the associated zero mode solutions, are straightforwardly derived by means of an analytical procedure. The results allow one to identify thick brane solutions that support internal structures and that can hold the ($3+1$)-dimensional gravity.

Tensor perturbations of Palatinif(R)branes

We investigate the thick brane model in Palatini $f(\mathcal{R})$ gravity. The brane is generated by a real scalar field with a scalar potential. We solve the system analytically and obtain a series of thick brane solutions for the $f(\mathcal{R})=\mathcal{R}+\alpha \mathcal{R}^2$-brane model. It is shown that tensor perturbations of the metric are stable for $df({\mathcal{R}})/d{\mathcal{R}}>0$. For nonconstant curvature solutions, the graviton zero mode can be localized on the brane, which indicates that the four-dimensional gravity can be recovered on the brane. Mass spectrum of graviton KK modes and their corrections to the Newtonian potential are also discussed.

Brane structure from a scalar field in general covariant Horava-Lifshitz gravity

In this paper we have considered the structure of the non-projectable Horava-Melby-Thompson (HMT) gravity to find braneworld scenarios. A relativistic scalar field is considered in the matter sector and we have shown how to reduce the equations of motion to first-order differential equations. In particular, we have studied thick brane solutions of both the dilatonic and Randall-Sundrum types.

Brane worlds in critical gravity

Recently, Lu and Pope proposed critical gravities in [Phys. Rev. Lett. 106, 181302 (2011)]. In this paper we construct analytic brane solutions in critical gravity with matter. The Gibbons-Hawking surface term and junction condition are investigated, and the thin and thick brane solutions are obtained. All these branes are embedded in five-dimensional anti-de Sitter spacetimes. Our solutions are stable against scalar perturbations, and the zero modes of scalar perturbations cannot be localized on the branes.

Equivalence between Born–Infeld tachyon and effective real scalar field theories for brane structures in warped geometry

An equivalence between Born–Infeld and effective real scalar field theories for brane structures is built in some specific warped space–time scenarios. Once the equations of motion for tachyon fields related to the Born–Infeld action are written as first-order equations, a simple analytical connection with a particular class of real scalar field superpotentials can be found. This equivalence leads to the conclusion that, for a certain class of superpotentials, both systems can support identical thick brane solutions as well as brane structures described through localized energy densities, T00(y), in the 5th dimension, y. Our results indicate that thick brane solutions realized by the Born–Infeld cosmology can be connected to real scalar field brane scenarios which can be used to effectively map the tachyon condensation mechanism.

“Critical” Cosmology in Higher Order Gravity

We construct the higher order terms of curvatures in Lagrangians of the scale factor in the D-dimensional Robertson-Walker metric, which are linear in the second derivative of the scale factor with respect to cosmic time. It is shown that they are composed of the Lovelock tensors at the first step; iterative construction yields arbitrarily high order terms. The relation to the former work on higher order gravity is discussed. Despite the absence of scalar degrees of freedom in cosmological models which come from our Lagrangian, it is shown that an inflationary behavior of the scale factor can be found. The application to the thick brane solutions is also studied.

A de Sitter tachyon thick braneworld

Among the multiple 5D thick braneworld models that have been proposed in the last years,in order to address several open problems in modern physics, there is a specific one involving atachyonic bulk scalar field. Delving into this framework, a thick braneworld with a cosmologicalbackground induced on the brane is here investigated. The respective field equations — derivedfrom the model with a warped 5D geometry — are highly non-linear equations, admitting anon-trivial solution for the warp factor and the tachyon scalar field as well, in a de Sitter 4Dcosmological background. Moreover, the non-linear tachyonic scalar field, that generates the branein complicity with warped gravity, has the form of a kink-like configuration. Notwithstanding, thenon-linear field equations restricting character does not allow one to easily find thick branesolutions with a decaying warp factor which leads to the localization of 4D gravity and othermatter fields. We derive such a thick brane configuration altogether in this tachyon-gravitysetup. When analyzing the spectrum of gravity fluctuations in the transverse traceless sector, the4D gravity is shown to be localized due to the presence of a single zero mode bound state,separated by a continuum of massive Kaluza-Klein (KK) modes by a mass gap. It contrasts withprevious results, where there is a KK massive bound excitation providing no clear physicalinterpretation. The mass gap is determined by the scale of the metric parameter H. Finally, thecorrections to Newton's law in this model are computed and shown to decay exponentially. It is infull compliance to corrections reported in previous results (up to a constant factor) withinsimilar braneworlds with induced 4D de Sitter metric, despite the fact that the warp factor andthe massive modes have a different form.

Thick brane solutions supported by two spinor fields

Stationary thick brane solutions supported by two spinor fields are considered. Two spinor fields are used here to exclude the off-diagonal components of the energy-momentum tensor of the spinor fields. The trapping of a test scalar field on the brane is also considered.