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 $f(R)=R+αR^2$. 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 $α$ 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.
In this paper, thick branes generated by mimetic scalar field are investigated. Three typical thick brane models are constructed and the linear tensor and scalar perturbations are analyzed. These branes have different inner structures, some of which are absent in general relativity. For each brane model, the solution is stable under both tensor and scalar perturbations. The tensor zero modes are localized on the branes, while the scalar perturbations do not propagate and they are not localized on the brane. As the branes split into multi sub-branes for specific parameters, the potentials of th…
We extend the idea of mimetic gravity to a Randall-Sundrum II braneworld model. As for the 4-dimensional mimetic gravity, we isolate the conformal degree of freedom of 5-dimensional gravity in a covariant manner. We assume the bulk metric to be made up of a non-dynamical scalar field $Φ$ and an auxiliary metric $\tilde{\cal{G}}_{AB}$ so that ${\cal{G}}_{AB}= \tilde{\cal{G}}^{CD}\,Φ_{,C}\,Φ_{,D}\,\tilde{\cal{G}}_{AB}$ where $A, B, ...$ are the bulk spacetime indices. Then we show that the induced conformal degree of freedom on the brane as an induced scalar field, plays the role of a mimetic fi…
In this paper, thick branes generated by the mimetic scalar field with Lagrange multiplier formulation are investigated. We give three typical thick brane background solutions with different asymptotic behaviors and show that all the solutions are stable under tensor perturbations. The effective potentials of the tensor perturbations exhibit as volcano potential, Poöschl-Teller potential, and harmonic oscillator potential for the three background solutions, respectively. All the tensor zero modes (massless gravitons) of the three cases can be localized on the brane. We also calculate the corre…
In this work, we investigate gravitational resonances in both single and double mimetic thick branes, which can provide a new way to detect the extra dimension. For the single brane model, we apply the relative probability proposed in [Phys. Rev. D. 80 (2009) 065019]. For the double brane model, we investigate the resonances quasi-localized on the double brane, on the sub-branes and between the sub-branes, respectively. To investigate the resonances quasi-localized on the double brane, we introduce two different definitions of the relative probability and find that the corresponding mass spect…
In this paper, we investigate thick branes generated by a scalar field in mimetic gravity theory. 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 analysed. 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…
We find new solutions to the Einstein-Maxwell equations in the presence of mimetic field in $ D $ dimensions, all of which are asymptotically Antide Sitter. We derive the solutions in five-dimensional spacetime, in detail. By extending the calculations to six and seven dimensions, we obtain a general form for solutions in dimensions larger than four. The results describe electrically charged static and rotating solutions, which have spherical, toroidal or cylindrical horizons. The solutions, depending on their global identifications, can be regarded as black holes, or black strings/branes. Som…
In this review, we give a brief introduction on the aspects of some extra dimension models and the five-dimensional thick brane models in extended theories of gravity. First, we briefly introduce the Kaluza-Klein theory, the domain wall model, the large extra dimension model, and the warped extra dimension models. Then some thick brane solutions in extended theories of gravity are reviewed. Finally, localization of bulk matter fields on thick branes is discussed.
In this paper, we investigate the localization of a five-dimensional vector field on a pure geometrical thick brane. In previous work, it was shown that a free massless vector field cannot be localized on such thick brane. Hence we introduce the interaction between the vector field and the background scalar field. Two types of couplings are constructed as examples. We get a typical volcano potential for the first type of coupling and a finite square-well-like potential for the second one. Both of the two types of couplings ensure that the vector zero mode can be localized on the pure geometric…
We study the procedure that allows to rewrite the actions of some modified gravity theories like mimetic gravity and Regge-Teitelboim embedding theory as Einstein-Hilbert actions with additional matter contributions. It turns out that this procedure can be applied to brane action, which lead to a polynomial brane action. We also examine the connection between this procedure and Polyakov trick in string theory.
This work deals with the presence of thick branes in a model with two source scalar fields that interact with one another in a very specific way. The model is new, capable of generating kinklike configurations that engender important modifications in the energy density of the system, inducing the presence of symmetric and asymmetric structures inside the brane.
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 dimensi…
We study two exactly solvable five-dimensional thick brane world models in pure metric $f(R)$ gravity. Working in the Einstein frame, we show that these solutions are stable against small linear perturbations, including the tensor, vector, and scalar modes. For both models, the corresponding gravitational zero mode is localized on the brane, which leads to the four-dimensional Newton's law; while the massive modes are nonlocalized and only contribute a small correction to the Newton's law at a large distance.
In this work we study braneworlds generated by several scalar fields. The investigation describes the necessary formalism to examine models and evaluate the conditions for the stability of the gravitational sector under linear perturbations. In particular, we develop a mechanism that help us investigate distinct situations controlled by two and by three fields, focusing on how the fields can be used to modify the internal structure of the brane.
In this work we investigate the issue of fermion localization and resonances in $(4,1)$-deformed branes constructed with one scalar field coupled with gravity. Such models provide us branes with internal structures that turns the gravitational interaction more effective for fermions aside the brane, increasing their lifetime. The coupling between the scalar field and spinors is a necessary condition for fermions to be localized on such branes. After performing a chiral decomposition of the five-dimensional spinor we found resonances with both chiralities. The correspondence between the spectra…
It has been found that the zero mode of a five-dimensional Elko spinor could be localized on branes by introducing a Yukawa-type coupling between the Elko spinor and the background scalar field or the Ricci scalar. However, the Yukawa-type coupling is not appropriate for all brane models. In this paper, we explore other localization mechanism for the Elko spinor by introducing the non-minimal coupling $f(ϕ)\mathfrak{L}_{Elko}$ between the five-dimensional Elko spinor and the background scalar field. We give the general expressions of the Elko zero mode and the function $f(ϕ)$. Through two thic…
One of the interesting open problems in the cosmological framework is applying quantum physics to the whole universe, consistently. Although different conceptual aspects of quantum cosmology are still very much alive, till now, all the attempts of obtaining a unique and well-defined version of quantum cosmology have been unfeasible. Motivated by what was mentioned above, in this paper, the quantum tunneling of thick brane is investigated by deriving the Wheeler-DeWitt equation and corresponding solutions. Besides, the cosmological analysis of the brane is studied based on two special cases of …
This work discuss the construction of braneworld solutions in modified gravity with Lagrange multipliers. We examine the general aspects of the model and present a first order formalism that help us to find analytic solutions of the equations of motion. We also investigate some explicit models, analyse linear stability of the metric and comment on how to relate models investigated in other works to the ones examined in the present study.
A thick brane model with Gauss-Bonnet action in a homogeneous anisotropic $D=(4+1+d)$ spacetime is studied. By choosing a concrete metric ansatz, we show that this spacetime is stable against linear tensor perturbations under certain conditions. The graviton zero modes are also given. Besides, we examine a particular example in six-dimensional spacetime with a given warp factor. The coupled background scalar field and its potential are solved analytically. Furthermore, the effective potential of the Kaluza-Klein modes of the graviton is also discussed. We found that the effective potential can…
In this work, we compute the corrections in the Newton's law of gravitation due to Kaluza-Klein gravitons in codimension-1 warped thick braneworld scenarios. We focus in some models recently proposed in the literature, the so-called asymmetric hybrid brane and compact brane. Such models are deformations of the $ϕ^4$ and sine-Gordon topological defects, respectively. Therefore we consider the branes engendered by such defects and we also compute the corrections in their cases. We use suitable numerical techniques to attain the mass spectrum and its corresponding eigenfunctions which are the ess…
The Palatini $f(|\hatΩ|)$ gravity is a generalized theory of the Eddington-inspired Born-Infeld gravity, where $Ω_{~N}^{K}\equivδ_{~N}^{K}+bg^{KL}R_{LN}(Γ)$ is an auxiliary tensor constructed with the spacetime metric $g$ and independent connection $Γ$. In this paper, we study $f(|\hatΩ|)$ theory with $f(|\hatΩ|)=|\hatΩ|^{\frac{1}{2}+n}$ in the thick brane scenario and give some constraints on the brane model. We finally found an analytic solution of the thick brane generated by a single scalar field. The behavior of the negative energy density denotes the localization of the thick brane at th…
Two co-dimensional thick brane-worlds are investigated in quite general terms for two intersecting scalar fields generating the extra dimension defect. In general, when one considers two co-dimensional thick brane-worlds, the warp factor is constructed as a string-like defect. Considering a twofold-warp factor constructed from two intersecting warp factors, an alternative bulk configuration is examined. With the brane localization thus driven by two crossing scalar fields, the possible solvable models obtained from such a two co-dimensional setup are systematically discussed. The obtained solu…
The nature of gravity and its strength compared with other forces are fundamental challenges faced by the actual science. A path to understanding the hierarchy problem of gravity consists in adding an extra dimension to Einstein-Hilbert's general relativity. Therefore, gravity would be the only force leaking through this region of spacetime also known as brane. Despite the success of the mathematical description for the hierarchy issue through simple thin branes, it is also possible to derive a consistent theory of gravity using thick branes. The present work unveils a new procedure to determi…
Spherically symmetric time-dependent solutions for the 5D system of a scalar field canonically coupled to gravity are obtained and identified as an extension of recent results obtained by Ahmed, Grzadkowskia and Wudkab. The corresponding cosmology of models with regularized branes generated by such a 5D scalar field scenario is also investigated. It has been shown that the anisotropic evolution of the warp factor and consequently the Hubble like parameter are both driven by the radial coordinate on the brane, which leads to an emergent thick brane-world scenario with spherically symmetric time…
We propose a codimension two warped braneworld model within the teleparallel $f(T)$ gravity. By assuming a global vortex as the source, we found a $l=0$ vortex solution that yields to a thick string-like brane. Asymptotically, the bulk geometry converges to an $AdS_6$ spacetime whose cosmological constant is produced by the torsion parameters. Furthermore, the torsion induces an $AdS-dS$ transition on the exterior region. Inside the brane core, the torsion produces an internal structure even for a single complex scalar field. As the torsion parameters vary, the brane undergoes a phase transiti…
In this paper, we study the thick brane scenario constructed in the recently proposed $f(T,\mathcal{T})$ theories of gravity, where $T$ is called the torsion scalar, and $\mathcal{T}$ is the trace of the energy-momentum tensor. We use the first-order formalism to find analytical solutions for models that include a scalar field as a source. In particular, we describe two interesting cases in which, in the first, we obtain a double-kink solution, which generates a splitting in the brane. In the second case, proper management of a kink solution obtained generates a splitting in the brane intensif…
This work deals with thick braneworld models, in an environment where the Ricci scalar is changed to accommodate the addition of two extra terms, one depending on the Ricci scalar itself, and the other, which takes into account the trace of the energy-momentum tensor of the scalar field that sources the braneworld scenario. We suppose that the scalar field engenders standard kinematics, and we show explicitly that the gravity sector of this new braneworld scenario is linearly stable. We illustrate the general results investigating two distinct models, focusing on how the brane profile is chang…
In this work, we present new soliton solutions for thick branes in $4+1$ dimensions. In particular, we consider brane models based on the sine-Gordon ($SG$), $φ^{4}$ and $φ^{6}$ scalar fields, which have broken $Z_{2}$ symmetry in some cases, and are responsible for supporting and stabilizing the thick branes. The origin of the symmetry breaking in these models resides in the fact that the modified scalar field potential may have non-degenerate vacuua. These vacuua determine the cosmological constant on both sides of the brane. We also study the geodesic equations along the fifth dimension, in…
