Energy momentum tensor of a quantized massless bulk spin-$\frac{1}{2}$ field in five dimensional warped cosmological spacetimes is studied. The four dimensional part of our model represents a warped cosmological thick brane and the scale of the extra dimension is time-dependent. We use a simple ansatz to solve the Dirac equation in the bulk that helps us to compare our results with the known four dimensional case. Renormalisation of the components of the energy momentum tensor is achieved using adiabatic regularization method. We compute the leading order finite contribution to the stress-energy tensor which is of adiabatic order six. The resulting energy and pressure densities explicitly show the effects of the so-called warping factor and the dynamic extra dimension on the created matter. We show how the energy density produced are localized to form 3-branes along the extra dimension.
Energy momentum tensor of a conformally coupled quantum scalar field in five dimensional warped cosmological spacetimes is studied. We look at situations where the four dimensional part represents a cosmological thick brane and the scale of the extra dimension is time dependent. Renormalization of the components of the energy momentum tensor is achieved using adiabatic regularization method. The resulting energy and pressure densities explicitly show the effects of warping and the dynamic extra dimension on the created matter. We discussed how the created matter may accumulate to form thick br…
Ellis-Bronnikov (EB) wormholes require violation of null energy conditions at the `throat'. This problem was cured by a simple modification of the `shape function', which introduces a new parameter $m\ge 2$ ($m=2$ corresponds to the EB model). This leads to a generalised (GEB) version. In this work, we consider a model where the GEB wormhole geometry is embedded in a five dimensional warped background. We studied the status of all the energy conditions in detail for both EB and GEB embedding. We present our results analytically (wherever possible) and graphically. Remarkably, the presence of d…
In this paper, we study massless braneworld black holes as gravitational lenses. We find the weak and the strong deflection limits for the deflection angle, from which we calculate the positions and magnifications of the images. We compare the results obtained here with those corresponding to Schwarzschild and Reissner-Nordstrom spacetimes, and also with those found in previous works for some other braneworld black holes.
The role of a bulk graviton in predicting the signature of extra dimensions through collider-based experiments is explored in the context of a multiply warped spacetime. In particular it is shown that in a doubly warped braneworld model, the presence of the sixth dimension, results in enhanced concentration of graviton Kaluza Klein (KK) modes compared to that obtained in the usual 5-dimensional Randall-Sundrum model. Also, the couplings of these massive graviton KK modes with the matter fields on the visible brane turn out to be appreciably larger than that in the corresponding 5- dimensional …
The stability of the modular field in a warped brane world scenario has been a subject of interest for a long time. Goldberger \& Wise ( GW ) proposed a mechanism to achieve this by invoking a massive scalar field in the bulk space-time neglecting the back-reaction. In this work, we examine the possibility of stabilizing the modulus without bringing in any external scalar field. We show that instead of flat 3-branes as considered in Randall-Sundrum ( RS ) warped braneworld model, if one considers a more generalized version of warped geometry with de-Sitter 3-brane, then the brane vacuum energy…
Hubble expansion in warped braneworld model is addressed in presence of more than one warped extra dimensions. It is shown that while the expansion depends on all the moduli, an exponential nature of the expansion of the scale factor emerges as a generic feature which is independent of the number of extra dimensions. Expression for the effective brane cosmological constant in such model has been derived. It is shown that similar to the 5-dimensional Randall-Sundrum model a fine tuning between the bulk cosmological constant and brane tension is required to obtain the desired cosmological consta…
We study the static, analytical solution of black holes in the warped DGP braneworld scenario. We show that the linearized field equations and matching conditions lead to solutions that are not compatible with Schwarzschild-(A)dS$_{(4)}$ solutions on the brane. This incompatibility is similar to vDVZ discontinuity in massive gravity theory. Following the standard procedure to remove this discontinuity, which firstly was proposed by Vainshtein, we keep some appropriate nonlinear terms in the field equations. This strategy has its origin in the fact that the spatial extrinsic curvature of the br…
A new family of five dimensional, R=0 braneworlds with asymmetric warp factors is proposed. Beginning with the invariance of the Ricci scalar for the general class of asymmetrically warped spacetimes we, subsequently specialise to the R=0 case. Solutions are obtained by choosing a particular relation (involving a parameter $ν$) between the warp factors. Symmetric warping arises as a special case (particular value of $ν$). Over a range of values of $ν$ the energy conditions for the matter stress energy are found to hold good. It turns out that the energy density and pressures required to suppor…
We generalize nested multiply warped braneworld models by incorporating non-zero brane curvature caused by an effective cosmological constant Ω 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 Ω < 0, resolution of the gauge hierarchy problem imposes a small upper bound on |Ω|, and can possibly lead to positivity of all the 3-brane tensions. For Ω > 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 ext…
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…
We show that quantum mechanical supersymmetries are emerged in Kaluza-Klein spectrum of linearized gravity in several warped backgrounds as a consequence of higher-dimensional general coordinate invariance. These emergent supersymmetries play an essential role for the spectral structure of braneworld gravity. We show that for the case of braneworld models with two codimension-1 branes the spectral pattern is completely determined only through the supersymmetries.
For an extension of the previous work on gravitational lensing by massless braneworld black holes, we investigate their microlensing phenomena and shadows and discuss how to distinguish them from standard Schwarzschild black holes and Ellis wormholes. Microlensing is known as the phenomenon in which luminosity amplification appears when a bright object passes behind a black hole or another massive object. We find that, for the braneworld black hole as well as for the Ellis wormhole, there appears luminosity reduction just before and after the amplification. This means that observation of such …
We investigate the 5D massless fermionic fields within the standing wave braneworld model. We show that in the case of increasing warp factor there exist localized left spinor field zero modes on the brane, while right fermion wave functions are not normalizable.
We examine the modulus stabilization mechanism of a warped geometry model with nested warping. Such a model with multiple moduli is known to offer a possible resolution of the fermion mass hierarchy problem in the standard model. A six dimensional doubly warped braneworld model under consideration admits two distinct moduli, with the associated warp factors dynamically generating different physical mass scales on four 3-branes. In order to address the hierarchy problem related to the Higgs mass, both moduli need to be stabilized around their desired values without any extreme fine tuning of pa…
Braneworld models with induced gravity have the potential to replace dark energy as the explanation for the current accelerating expansion of the Universe. The original model of Dvali, Gabadadze and Porrati (DGP) demonstrated the existence of a ``self--accelerating'' branch of background solutions, but suffered from the presence of ghosts. We present a new large class of braneworld models which generalize the DGP model. Our models have negative curvature in the bulk, allow a second brane, and have general brane tensions and localized curvature terms. We exhibit three different kinds of ghosts,…
We study the braneworld theory constructed by multi scalar fields. The model contains a smooth and infinitely large extra dimension, allowing the background fields propagating in it. We give a de Sitter solution for the four-dimensional cosmology as a good approximation to the early universe inflation. We show that the graviton has a localizable massless mode, and a series of continuous massive modes, separated by a mass gap. There could be a normalizable massive mode, depending on the background solution. The gravitational waves of massless mode evolve the same as the four dimensional theory,…
A generalized Randall sundrum model in six dimensional bulk is studied in presence of non-flat 3-branes at the orbifold fixed points. The warp factors for this model is determined in terms of multiple moduli and brane cosmological constant. We show that the requirements of a vanishingly small cosmological constant on the visible brane along with non-hierarchical moduli, each with scale close to Planck length, lead to a scenario where the 3-branes can not have any intermediate scale and have energy scales either close to Tev or close to Planck scale. Such a scenario can address both the gauge h…
In this paper, we investigate gravitational waves as metric perturbations around a general warped 5-dimensional background. We find an analytical solution in Randall-Sundrum braneworld model and analyze the implications of braneworld models in the gravitational waves propagation.
The `braneworld' (described by the usual worldvolume action) is a D dimensional timelike surface embedded in a N dimensional ($N>D$) warped, nonfactorisable spacetime. We first address the conditions on the warp factor required to have an extremal flat brane in a five dimensional background. Subsequently, we deal with normal deformations of such extremal branes. The ensuing Jacobi equations are analysed to obtain the stability condition. It turns out that to have a stable brane, the warp factor should have a minimum at the location of the brane in the given background spacetime. To illustrate …
We consider a braneworld model in which an anisotropic brane is embedded in a dilatonic background. We solve the background solutions and study the behavior of the perturbations when the universe evolves from an inflationary Kasner phase to a Minkowski phase. We calculate the massless mode spectrum, and find that it does not differ from what expected in standard four-dimensional cosmological models. We then evaluate the spectrum of both light (ultrarelativistic) and heavy (nonrelativistic) massive modes, and find that, at high energies, there can be a strong enhancement of the Kaluza-Klein spe…
We investigate the stability of the extra dimensions in a warped, codimension two braneworld that is based upon an Einstein-Maxwell-dilaton theory with a non-vanishing scalar field potential. The braneworld solution has two 3-branes, which are located at the positions of the conical singularities. For this type of brane solution the relative positions of the branes (the shape modulus) is determined via the tension-deficit relations, if the brane tensions are fixed. However, the volume of the extra dimensions (the volume modulus) is not fixed in the context of the classical theory, implying we …
We study linearized gravity in a six-dimensional Einstein-Maxwell model of warped braneworlds, where the extra dimensions are compactified by a magnetic flux. It is difficult to construct a strict codimension two braneworld with matter sources other than pure tension. To overcome this problem we replace the codimension two defect by an extended brane, with one spatial dimension compactified on a Kaluza-Klein circle. Our background is composed of a warped, axisymmetric bulk and one or two branes. We find that weak gravity sourced by arbitrary matter on the brane(s) is described by a four-dimens…
We explore the possibilities of constructing bulk spacetimes in five dimensions for warped braneworld models with a spatially flat Friedmann-Robertson-Walker (FRW) line element on the 3-brane and with a time-dependent extra dimension. Our first step in this direction involves looking at the status of energy conditions when such a bulk line element is assumed. We check these conditions by analysing the relevant inequalities, for specific functional forms (chosen to satisfy certain desirable features) of the warp factor, the cosmological scale factor and the extra-dimensional scale factor. Subse…
The static potential for a massless scalar field shares the essential features of the scalar gravitational mode in a tensorial perturbation analysis about the background solution. Using the fluxbrane construction of [8] we calculate the lowest order of the static potential of a massless scalar field on a thin brane using series solutions to the scalar field's Klein Gordon equation and we find that it has the same form as Newton's Law of Gravity. We claim our method will in general provide a quick and useful check that one may use to see if their model will recover Newton's Law to lowest order …
We investigate the one-loop corrections at zero, as well as finite temperature, of a scalar field taking place in a braneworld motived warped background. After to reach a well defined problem, we calculate the effective action with the corresponding quantum corrections to each case.
We study a six-dimensional braneworld model with infinite warped extra dimensions in the case where the four-dimensional brane is described by a topological vortex of a U(1) symmetry-breaking Abelian Higgs model in presence of a negative cosmological constant. A detailed analysis of the microscopic parameters leading to a finite volume space-time in the extra dimensions is numerically performed. As previously shown, we find that a fine-tuning is required to avoid any kind of singularity on the brane. We then discuss the stability of the vortex by investigating the scalar part of the gauge-inva…
We reinvestigate the thermodynamics of black objects (holes and strings) in four-dimensional braneworld models that are originally constructed by Emparan, Horowitz and Myers based on the anti-de Sitter (AdS) C-metric. After proving the uniqueness of slicing the AdS C-metric, we derive thermodynamic quantities of the black objects by means of the Euclidean formulation and find that we have no necessity of requiring any regularization to calculate their classical action. We show that there exist the Bekenstein-Hawking law and the thermodynamic first law. The thermodynamic mass of the localized b…
In this paper we first obtain Friedmann equations for the $(n-1)$-dimensional brane embedded in the $(n+1)$-dimensional bulk, with intrinsic curvature term of the brane included in the action (DGP model). Then, we show that one can always rewrite the Friedmann equations in the form of the first law of thermodynamics, $dE=TdS+WdV$, at apparent horizon on the brane, regardless of whether there is the intrinsic curvature term on the brane or a cosmological constant in the bulk. Using the first law, we extract the entropy expression of the apparent horizon on the brane. We also show that in the ca…
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 fi…
We study the Friedmann equation for the warped codimension-two braneworld background which most closely resembles the Randall-Sundrum model. Extra matter on the (Planck) 4-brane, with equation of state p_θ=(α-1)ρfor the azimuthal pressure, is required to satisfy the junction conditions. For 1 < α< 5, we show that there are two static solutions to the Einstein equations for given values of the brane stress-energies. Close to the static solutions, the relation between Hubble expansion rate H and brane tension reproduces the standard 4D result for small H, but exhibits unusual deviations when H i…
In this paper, we have considered gravity in a 5-dimensional warped product space-time with a time-dependent warp factor, time-dependent extra dimension and a bulk cosmological constant. The braneworld is described by a spatially flat FRW-type metric. The five-dimensional field equations have been constructed and solved for various cases of the warp factor and the extra-dimensional scale factor, starting from very general type of the metric and then reducing down to specific cases. In the low energy regime, a stabilized bulk with constant curvature has been considered, from which the cosmologi…
This work deals with braneworld models in the presence of scalar fields in a five-dimensional warped geometry with a single extra dimension of infinite extent. We consider generalized models in the presence of the Ricci scalar, the trace of the stress-energy tensor and the cuscuton contribution. The models describe novel braneworld scenarios and the investigations consider distinct possibilities, from which we show how the brane may change to become thinner, although keeping gravitational stability and the gravity zero mode under strict control. Moreover, we did not identify any split behavior…
We investigate Gaussian warped five-dimensional thick braneworlds. Identification of the graviton's wave function (squared) in the extra-dimension with a probability distribution function leads to a straightforward probabilistic interpretation of braneworlds. The extra-coordinate $y$ is regarded as a Gaussian-distributed random variable. Hence, all of the field variables and operators which depend on $y$ are, also, randomly distributed. Four-dimensional measurable (macroscopic) quantities are identified with the corresponding averaged values over the Gaussian distribution. The present scenario…
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.
After incorporating the f(R) gravity into the general braneworld sum rules scope, it is shown that some particular class of warped five dimensional nonlinear braneworld models, which may be interesting for the hierarchy problem solution, still require a negative tension brane. For other classes of warp factors (suitable and not suitable for approaching the hierarchy problem) it is not necessary any negative brane tension in the compactification scheme. In this vein, it is argued that in the bulk f(R) gravity context, some types of warp factors may be useful for approaching the hierarchy proble…
We consider a 3-brane embedded in a warped 5-dimensional background with a dilaton and a Kalb-Ramond 2-form. We show that it is possible to find static solutions of the form of charged dS/AdS-like black hole with horizon which could have a negative mass parameter. The motion of the 3-brane in this bulk generates an effective 4-dimensional bouncing cosmology induced by the negative dark radiation term. This model avoids the instability that arises for bouncing brane in a Reissner-Nordstrøm-AdS bulk.
In this paper we address the issue of finding braneworld solutions in a five-dimensional Horndeski gravity and the mechanism of gravity localization into the brane via ``almost massless modes'' for suitable values of the Horndeski parameters. We compute the corrections to the Newtonian potential and discuss the limit where four-dimensional gravity is recovered.
We study cosmological inflation on a warped DGP braneworld where inflaton field is non-minimally coupled to induced gravity on the brane. We present a detailed calculation of the perturbations and inflation parameters both in Jordan and Einstein frame. We analyze the parameters space of the model fully to justify about the viability of the model in confrontation with recent observational data. We compare the results obtained in these two frames also in order to judge which frame gives more acceptable results in comparison with observational data.
We study braneworlds in a five dimensional bulk, where cosmological expansion is mimicked by motion through AdS$_5$. We show that the five dimensional graviton reduces to the four dimensional one in the late time approximation of such braneworlds. Inserting a fixed regulator brane far from the physical brane, we investigate quantum graviton production due to the motion of the brane. We show that the massive Kaluza-Klein modes decouple completely from the massless mode and they are not generated at all in the limit where the regulator brane position goes to infinity. In the low energy limit, th…
In the braneworld scenario ordinary standard model matter and on-gravitational fields are confined by some trapping mechanism to the 4-dimensional universe constituting the D3-branes which are embedded in a (4 + n)-dimensional manifold referred to as the bulk (n being the number of extra dimensions). The notion of particle confinement is necessary for theories with non-compact extra dimensions, otherwise, the particles would escape from our 4-dimensional world along unseen directions. In this paper, we have considered a five-dimensional warped product space-time having an exponential warping f…
We study the properties of gravity and bulk fields living in a torsion warped braneworld. The torsion is driven by a background vector whose norm provides a source for the bulk cosmological constant. For a vector as the derivative of a scalar field, we find new isotropic and anisotropic thick brane geometries. We analyse the features of bosonic and fermionic fields in this isotropic and in standing wave scenarios. The background vector provides nonminimal coupling between the field and the geometry leading to modifications in the Kaluza-Klein states. The spinor connection is modified by the to…
We consider a new braneworld model with a bulk scalar field coupled to gravity. The bulk scalar action is inspired by the proposed low energy effective action around the tachyon vacuum. A class of warped geometries representing solutions of this Einstein-scalar system for a specific scalar potential is found. The geometry is non singular with a decaying warp factor and a negative Ricci curvature. The solution of the hierarchy problem is obtained using this type of warping. Though qualitatively similar to the usual Randall--Sundrum I model there are interesting quantitative differences. Additio…
If our Universe is a 3+1 brane in a warped 4+1 dimensional bulk so that its expansion can be understood as the motion of the brane in the bulk, the time dependence of the boundary conditions for arbitrary bulk fields can lead to particle creation via the dynamical Casimir effect. In this talk I report results for the simplest such scenario, when the only particle in the bulk is the graviton and the bulk is the 5 dimensional anti-de Sitter spacetime.
We have studied the stability of wormhole geometries, under massless scalar, electromagnetic and axial gravitational perturbations, in the context of higher dimensional spacetimes. Intriguingly, the construction of a wormhole spacetime in the presence of higher dimensions, known as braneworld wormholes, \emph{does not} require the existence of exotic matter fields, unlike the scenario in four spacetime dimensions. Being a nonvacuum spacetime, the effective potential experienced by the axial gravitational perturbation differs considerably from the scenarios involving black holes. In particular,…
Within the 5D standing wave braneworld model numerical solutions of the equations for matter fields with various spins are found. It is shown that corresponding action integrals are factorizable and convergent over the extra coordinate, i.e. 4D fields are localized on the brane. We find that only left massless fermions are localized on the brane, while the right fermions are localized in the bulk. We demonstrate also quantization of Kaluza-Klein excited modes in our model.
The new class of the non-stationary solutions to the system of N-dimensional equations for coupled gravitational and massless scalar field is found. The model represents a single (N-1)-brane in a space-time with one large (infinite) and (N-5) small (compact) space-like extra dimensions. In some particular cases the model corresponds to the gravitational and scalar field standing waves bounded by the brane. These braneworlds can be relevant in string and other higher dimensional models.
The low energy regime of 5D braneworld models with a bulk scalar field is studied. The setup is rather general and includes the Randall-Sundrum and dilatonic braneworlds models as particular cases. We discuss the cosmological evolution of the system and conclude that, in a two brane system, the negative tension brane is generally expected to evolve towards a null warp-factor state. This implies, for late time cosmology, that both branes end up interacting weakly. We also analyze the observational constraints imposed by solar-system and binary-pulsar tests on the braneworld configuration. This …
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 a tachyonic bulk scalar field. Delving into this framework, a thick braneworld with a cosmological background induced on the brane is here investigated. The respective field equations --- derived from the model with a warped 5D geometry --- are highly non-linear equations, admitting a non-trivial solution for the warp factor and the tachyon scalar field as well, in a de Sitter 4D cosmological background. Moreover…
We study a spin 1/2 fermion in a teleparallel f(T) domain-wall thick braneworld. By assuming a non-minimal coupling of fermion to the torsion, a geometric alternative to the Yukawa coupling is found. The torsion parameters control the width of the massless Kaluza-Klein mode and the properties of the analogue quantum-potential near the origin. The non-normalized massive fermionic modes are also analyzed.
In this work the gravitational Kaluza-Klein (KK) modes are analysed on string-like braneworlds in six dimensions, namely the thin string-like Gherghetta-Shaposhnikov (GS) and the thick string-cigar model. We find a new massless mode in both modes satisfying the respective Schroedinger equation. By means of numerical analysis for both models, a complete graviton spectrum and eigenfunctions is attained. Besides the linear regime, the KK spectrum exhibits a decreasing behavior with an asymmetric mass gap with respect to the massless mode. The discontinuity is bigger in the GS model, and it is inv…
We show the dynamical stability of a six-dimensional braneworld solution with warped flux compactification recently found by the authors. We consider linear perturbations around this background spacetime, assuming the axisymmetry in the extra dimensions. The perturbations are expanded by scalar-, vector- and tensor-type harmonics of the four-dimensional Minkoswki spacetime and we analyze each type separately. It is found that there is no unstable mode in each sector and that there are zero modes only in the tensor sector, corresponding to the four-dimensional gravitons. We also obtain the firs…
We study the tidal deformations of various known black hole and wormhole solutions in a simple context of warped compactification -- Randall-Sundrum theory in which the four-dimensional spacetime geometry is that of a brane embedded in five-dimensional Anti-de Sitter spacetime. The linearized gravitational perturbation theory generically reduces to either an inhomogeneous second-order ODE or a homogeneous third-order ODE of which indicial roots associated with an expansion about asymptotic infinity can be related to Tidal Love Numbers. We describe various tidal-deformed metrics, classify their…
