We consider a modified gravity fluid on a Randall-Sundrum II brane situated at y=0, the action containing a power αof the scalar curvature. As is known from 4D spatially flat modified gravity, the presence of a bulk viscosity may drive the cosmic fluid into the phantom region (w < -1) and thereafter inevitably into the Big Rip singularity, even it is initially nonviscous and lies in the quintessence region (w > -1). The condition for this to occur is that the bulk viscosity contains the power (2α-1) of the scalar expansion. We combine this with the 5D RS II model, and find that the Big Rip, occurring for α> 1/2, carries over to the metric for the bulk metric, |y|>0. Actually, the scale factors on the brane and in the bulk become simply proportional to each other.
This article is devoted to the application of the holographic principle to describe Rip brane cosmological models in the presence of a bulk viscosity. We make use of the generalized infrared-cutoff holographic dark energy, introduced by Nojiri and Odintsov We consider various examples: Rip brane cosmology corresponding to the Little Rip case, asymptotic de Sitter theory, and the so-called Big Freeze theory leading to a singularity. Analytical expressions for infrared cutoffs, as well as the particle and the future horizons at the brane, are obtained. The equations for energy conservation on th…
We consider the dynamics of a viscous cosmological fluid in the generalized Randall-Sundrum model for an anisotropic, Bianchi type I brane. To describe the dissipative effects we use the Israel-Hiscock-Stewart full causal thermodynamic theory. By assuming that the matter on the brane obeys a linear barotropic equation of state, and the bulk viscous pressure has a power law dependence on the energy density, the general solution of the field equations can be obtained in an exact parametric form. The obtained solutions describe generally a non-inflationary brane world. In the large time limit the…
We consider the dynamics of a viscous cosmological fluid in the generalized Randall-Sundrum model for an isotropic brane. To describe the dissipative effects we use the Israel-Hiscock-Stewart full causal thermodynamic theory. In the limiting case of a stiff cosmological fluid with pressure equal to the energy density, the general solution of the field equations can be obtained in an exact parametric form for a cosmological fluid with constant bulk viscosity and with a bulk viscosity coefficient proportional to the square root of the energy density, respectively. The obtained solutions describe…
We assume a flat brane located at y=0, surrounded by an AdS space, and consider the 5D Einstein equations when the energy flux component of the energy-momentum tensor is related to the Hubble parameter through a constant Q. We calculate the metric tensor, as well as the Hubble parameter on the brane, when Q is small. As a special case, if the brane is tensionless, the influence from Q on the Hubble parameter is absent. We also consider the emission of gravitons from the brane, by means of the Boltzmann equation. Comparing the energy conservation equation derived herefrom with the energy conser…
Singularities in the dark energy late universe are discussed, under the assumption that the Lagrangian contains the Einstein term R plus a modified gravity term R^α, where αis a constant. The 4D fluid is taken to be viscous and composed of two components, one Einstein component where the bulk viscosity is proportional to the scalar expansion θ, and another modified component where the bulk viscosity is proportional to the power θ^{2α-1}. Under these conditions it is known from earlier that the bulk viscosity can drive the fluid from the quintessence region (w > -1) into the phantom region (w<-…
We consider how the five-dimensional Randall-Sundrum (one-brane) theory becomes modified when account is taken of the bulk viscosity of the cosmic fluid on the brane. We focus on the plasma era between $10^{12}$K (muon pair annihilation) to about $5\times 10^9$K (electron-positron annihilation), which includes the first order quark-hadron transition beginning at an energy density of about $5\times 10^9\rm MeV^4$. Various possibilities are examined for modeling the bulk viscosity, preference being at the end given to the results calculated from relativistic kinetic theory. According to this, th…
We investigate the role of bulk viscous pressure on the warm inflationary modified Chaplygin gas in brane-world framework in the presence of standard scalar field. We assume the intermediate inflationary scenario in strong dissipative regime and constructed the inflaton, potential, entropy density, slow-roll parameters, scalar and tensor power spectra, scalar spectral index and tensor-to-scalar ratio. We develop various trajectories such as $n_s - N$, $n_s - r$ and $n_s - α_s$ (where $n_s$ is the spectral index, $α_s$ is the running of spectral index, $N$ is the number of e-folds and $r$ is te…
In this paper, we have constructed the cosmological model of the universe in a two fluids environment with a newly developed mathematical formalism. In order to construct the model Binachi type V (BV) space time is considered with a time varying deceleration parameter. Both the fluids, the viscous fluid and the dark energy (DE) fluid have shown their dominance respectively in early time and late time of the cosmic evolution. The scale factor that simulates the cosmic transition based on the value of the bulk viscous coefficient. Within the developed formalism, a general form of the skewness pa…
In this paper, we have investigated the possibility to have inflation from inhomogeneous viscous fluids by taking into account the brane correction coming from string-inspired five dimensional Einsten's gravity. We have realized several kinds of viable solutions for early-time acceleration. At the end of inflation, the classical Einstein's gravity is recovered and fluids produce decelerated expansion.
The presence of a bulk viscosity for the cosmic fluid on a single Randall-Sundrum brane is considered. The spatial curvature is assumed to be zero. The five-dimensional Friedmann equation is derived, together with the energy conservation equation for the viscous fluid. These governing equations are solved for some special cases: (i) in the low-energy limit when the matter energy density is small compared with brane tension; (ii) for a matter-dominated universe, and (iii) for a radiation-dominated universe. Rough numerical estimates, for the extreme case when the universe is at its Planck time,…
Branes are embedded surfaces in a given background (bulk) spacetime. Assuming a warped bulk, we investigate, in analogy with the case for geodesics, the notion of {\em focusing} of families of such embedded, extremal 3--branes in a five dimensional background . The essential tool behind our analysis, is the well-known generalised Raychaudhuri equations for surface congruences. In particular, we find explicit solutions of these equations, which seem to show that families of 3--branes can focus along lower dimensional submanifolds depending on where the initial expansions are specified. We concl…
We carefully investigate the modified Einstein's field equation in a four dimensional (3-brane) arbitrary manifold embedded in a five dimensional Non-Riemannian bulk spacetime with a noncompact extra dimension. In this context the Israel-Darmois matching conditions are extended assuming that the torsion in the bulk is continuous. The discontinuity in the torsion first derivatives are related to the matter distribution through the field equation. In addition, we develop a model that describes a flat FLRW model embedded in a 5-dimensional de Sitter or Anti de Sitter, where a 5-dimensional cosmol…
We have derived effective gravitational field equations on a lower dimensional hypersurface (known as a brane), placed in a higher dimensional bulk spacetime for both Einstein and $f(\mathcal{R})$ gravity theories. We have started our analysis on $n$-dimensional bulk from which the effective field equations on a $(n-1)$-dimensional brane has been obtained by imposing $Z_{2}$ symmetry. Subsequently, we have arrived at the effective equations in $(n-2)$-dimensions starting from the effective equations for $(n-1)$ dimensional brane. This analysis has been carried forward and is used to obtain the…
We present a new general class of four-dimensional effective field theories with interesting global symmetry groups. These theories arise from purely gravitational actions for (3+1)-dimensional branes embedded in higher dimensional spaces with induced gravity terms. The simplest example is the well known Galileon theory, with its associated Galilean symmetry, arising as the limit of a DGP brane world. However, we demonstrate that this is a special case of a much wider range of theories, with varying structures, but with the same attractive features such as second order equations. In some circu…
We take advantage of the Shiromizu et al. covariant formalism to find out the brane properties originating from the five dimensional bulk spacetime. Making a different choice for the conformal factor $e^{-2b(z)}$ compared to Estrada [24], we reach a new solution with a lot of interesting properties, where $b(z) = ln(1/\sqrt{cosh2μz})$. The non-local tensor $E_{ab}$ rooted from the 5-dimensional Riemann tensor gives an anisotropic stress energy tensor on the brane with positive energy density and negative radial pressure. The BH on the brane looks like a black string in the 5-dimensional space,…
While in general relativity black holes can be freely embedded into a cosmological background, the same problem in brane-worlds is much more cumbersome. We present here the results obtained so far in the explicit constructions of such space-times. We also discuss gravitational collapse in this context.
The braneworlds models were inspired partly by Kaluza-Klein's theory, where both the gravitational and the gauge fields are obtained from the geometry of a higher dimensional space. The positive aspects of these models consist in perspectives of modifications it could bring in to particle physics, such as: unification in a TeV scale, quantum gravity in this scale and deviation of Newton's law for small distances. One of the principles of these models is to suppose that all space-times can be embedded in a bulk of higher dimension. The main result in these notes is a theorem showing a mathemati…
Dirac's method for variations of a brane embedded in co-dimension one is demonstrated. The variation in the location of the brane invokes a rest frame formulation of the 'sandwiched' brane action. We first demonstrate the necessity of this method by re-deriving Snell's law. Second, we apply the method to a general $N$-dimensional brane embedded in co-dimension one bulk in the presence of gravity. We re-derive the brane equations: (i) Israel junction condition, (ii) Energy/momentum conservation on the brane, and (iii) Geodetic-type equation for the brane.
The brane-worlds model was inspired partly by Kaluza-Klein's theory, where the gravitation and the gauge fields are obtained of a geometry of higher dimension (bulk). Such a model has been showing positive in the sense of we find perspectives and probably deep modifications in the physics, such as: Unification in a scale TeV, quantum gravity in this scale and deviation of Newton's law for small distances. One of the principles of this model is to suppose a space-time embedded in a bulk of high dimension. In this note it is shown, basing on the theorem of Collinson-Szekeres, that the space-time…
We study the massless scalar, Dirac and electro-magnetic fields propagating on a 4D-brane, which is embedded in higher dimensional Gauss-Bonnet space-time. We calculate, in time-domain, the fundamental quasi-normal modes of a spherically symmetric black hole for such fields. We observe also a universal behavior, independent on a field and value of the Gauss-Bonnet parameter, at asymptotically late time.
Braneworld scenarios consider our observable universe as a brane embedded in a 5D space, named bulk. In this work, I derive the field equations of a braneworld model in a generalized theory of gravitation, namely $f(R,T)$ gravity, with $R$ and $T$, representing the Ricci scalar and the trace of the energy-momentum tensor, respectively. The cosmological parameters obtained from this approach are in agreement with recent constraints from Supernovae Ia data combined with baryon acoustic oscillations and cosmic microwave background observations, favouring such an alternative description of the uni…
We show that D=4 Schwarzschild black holes can arise from a doublet of Euclidean D3-antiD3 pairs embedded in D=10 Lorentzian spacetime. By starting from a D=10 type IIB supergravity description for the D3-antiD3 pairs and wrapping one of them over an external 2-sphere, we derive all vacuum solutions compatible with the symmetry of the problem. Analysing under what condition a Euclidean brane configuration embedded in a Lorentzian spacetime can lead to a time-independent spacetime, enables us to single out the embedded D=4 Schwarzschild spacetime as the unique solution generated by the D3-antiD…
We discuss a new mechanism of obtaining a period of cosmological inflation in the context of string theory. This mechanism is based on embedded defects which form dynamically on higher dimensional D-branes. Such defects generate topological inflation, but unlike topological inflation from stable defects, here there is a natural graceful exit from inflation: the decay of the embedded defect. We demonstrate the idea in the context of a brane-antibrane annihilation process. The graceful exit mechanism suggested here applies generically to all realizations of inflation on D-branes.
We give the equations of motion for a self-gravitating Dirac p-brane embedded in an even co-dimension spacetime. The dynamics of the bulk are dictated by Lovelock gravity and permit matching conditions, even when the codimension is strictly greater than 2. We show that the equations of motion involve both induced Lovelock densities on the brane and regular extrinsic curvature terms. The brane dynamics can be derived from an exact (p+1)-dimensional induced action. The Dirac charge is carried by an overall (solid) angle defect which sets the Planck scale on the brane. In particular, if the codim…
It has recently been proposed that our universe is a three-brane embedded in a higher dimensional spacetime. Here I show that black holes on the brane, black strings intersecting the brane, and gravitational waves propagating in the bulk induce an effective energy-momentum tensor on the brane that contains negative energy densities.
We introduce brane-worlds with non-constant tension, strenghtening the analogy with fluid membranes, which exhibit a temperature-dependence according to the empirical law established by Eötvös. This new degree of freedom allows for evolving gravitational and cosmological constants, the latter being a natural candidate for dark energy. We establish the covariant dynamics on a brane with variable tension in full generality, by considering asymmetrically embedded branes and allowing for non-standard model fields in the 5-dimensional space-time. Then we apply the formalism for a perfect fluid on a…
We consider four-dimensional de Sitter, flat and anti de Sitter branes embedded in a six-dimensional bulk spacetime whose dynamics is dictated by Lovelock theory. We find, applying a generalised version of Birkhoff's theorem, that all possible maximally symmetric braneworld solutions are embedded in Wick-rotated black hole spacetimes of Lovelock theory. These are warped solitonic spaces, where the horizons of the black hole geometries correspond to the possible positions of codimension-2 branes. The horizon temperature is related via conical singularities to the tension or vacuum energy of the…
Cosmological consequences of the brane world scenario are reviewed in a pedagogical manner. According to the brane world idea, the standard model particles are confined on a hyper--surface (a so--called brane), which is embedded in a higher--dimensional spacetime (the so--called bulk). We begin our review with the simplest consistent brane world model: a single brane embedded in a five--dimensional Anti-de Sitter space--time. Then we include a scalar field in the bulk and discuss in detail the difference with the Anti-de Sitter case. The geometry of the bulk space--time is also analysed in som…
We review some recent results obtained from the application of the Gauss-Codazzi formalism to brane-worlds models in the Brans-Dicke gravity. The cases of 4-branes embedded in a six-dimensional with and without $\mathbb{Z}_{2}$ symmetry are both analyzed.
In brane-worlds, our universe is assumed to be a submanifold, or brane, embedded in a higher-dimensional bulk spacetime. Focusing on scenarios with a curved five-dimensional bulk spacetime, I discuss their gravitational and cosmological properties.
We consider spherically symmetric matter configurations on a four dimensional "brane" embedded in a five dimensional $Z_2$-symmetric "bulk". We write the junction conditions between the interior and exterior of these "stars", treat a couple of static examples in order to point out the differences with ordinary four dimensional Einstein gravity, consider briefly a collapse situation and conclude with the importance of a global view including asymptotic and regularity conditions in the bulk.
We explore the tensor perturbation of the $f(T)$ brane embedded in an AdS$_5$ spacetime. With the transverse-traceless condition, we get the tensor perturbation equation of the $f(T)$ brane and show that the stability of this brane system can be ensured. In addition, we take $ f(T)=T+αT^2$ as an example to analyse the localization problem of the graviton zero mode. It is shown that the graviton zero mode can be localized on the brane.
We consider the dynamics of a 3-brane embedded in an extra-dimensional Tolman-Bondi Universe where the origin of space plays a special role. The embedding is chosen such that the induced matter distribution on the brane respects the spherical symmetry of matter in the extra dimensional space. The mirage cosmology on the probe brane is studied, resulting in an inhomogeneous and anisotropic four dimensional cosmology where the origin of space is also special. We then focus on the spatial geometry around the origin and show that the induced geometry, which is initially inhomogeneous and anisotrop…
Starting with the Nambu-Goto action of the braneworld embedded in a curved bulk, we derive the precise expressions for the quantum induced effects due to small fluctuations of the brane. To define the brane fluctuations invariantly, we introduce the Riemannian coordinate system for the subspace normal to the braneworld. It will turn out that we can systematically incorporate the effects of bulk curvature, and that the induced effects depend on the extrinsic curvature and the normal-connection gauge field as well as on bulk curvature components at the brane.
We study the cosmology of a 5-dimensional brane, which represents a regularization of a 4-dimensional codimension-2 brane, embedded in a conical bulk. The brane is assumed to be tensional, and to contain a curvature term. Cosmology is obtained by letting the brane move trough the bulk, and implementing dynamical junction conditions. Our results shows that, with suitable choices of the parameters, the resulting cosmological dynamics mimics fairly well standard 4-dimensional cosmology.
We present the study of a two 3-branes system embedded in a 5-dimensional space-time in which the fifth dimension is compacted on a $S^{1}/Z_{2}$ orbifold and the space between the two branes is vacuum. Assuming isotropic and homogeneous space time, we probe that the dynamics of the visible brane is affected by the dynamics of the hidden brane and the possible components which fills it. We study two different cases: assuming a constant equation of state and inflationary scalar field, and its possible consequences in the brane evolution.
We consider branes embedded in spacetimes of codimension one and two, with a warped metric tensor for the subspace parallel to the brane. We study a variety of brane-world solutions arising by introducing a Schwarzschild-like black hole metric on the brane and we investigate the properties of the corresponding higher-dimensional spacetime. We demonstrate that normalizable bulk modes lead to a vanishing flow of energy through the naked singularities. From this point of view, these singularities are harmless.
Solutions of geodesic equations describing propagation of gravitons in the bulk are studied in a cosmological model with one extra dimension. Brane with matter is embedded in the bulk. It is shown that in the period of early cosmology gravitons emitted from the brane to the bulk under certain conditions can return back to the brane. The model is discussed in two alternative approaches: (i) brane with static metric moving in the AdS space, and (ii) brane located at a fixed position in extra dimension with non-static metric. Transformation of coordinates from the one picture to another is perfor…
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.
We present the study of two 3-brane system embedded in a 5-dimensional space-time in which the fifth dimension is compactified on a $S^{1}/Z_{2}$ orbifold. Assuming isotropic, homogeneous, and static branes, it can be shown that the dynamics of one brane is dominated by the other one when the metric coefficients have a particular form. We study the resulting cosmologies when one brane is dominated by a given single-fluid component.
We derive the effective cosmological equations for a non-$\mathbb{Z}_2$ symmetric codimension one brane embedded in an arbitrary D-dimensional bulk spacetime, generalizing the $D=5,6$ cases much studied previously. As a particular case, this may be considered as a regularized codimension (D-4) brane avoiding the problem of curvature divergence on the brane. We apply our results to the case of spherical symmetry around the brane and to partly compactified AdS-Schwarzschild bulks.
We disclose the deep connection between the thermodynamics and gravity in a general braneworld model with curvature correction terms on the brane and in the bulk, respectively. We show that the Friedmann equations on the 3-brane embedded in the 5D spacetime with curvature correction terms can be written directly in the form of the first law of thermodynamics on the apparent horizon. Using the first law, we extract the entropy expression of the apparent horizon on the brane, which is useful in studying the thermodynamical properties of the black hole horizon on the brane in Gauss-Bonnet gravity…
We canonically quantize the dynamics of the brane universe embedded into the five-dimensional Schwarzschild-anti-deSitter bulk space-time. We show that in the brane-world settings the formulation of the quantum cosmology, including the problem of initial conditions, is conceptually more simple than in the 3+1-dimensional case. The Wheeler-deWitt equation is a finite-difference equation. It is exactly solvable in the case of a flat universe and we find the ground state of the system. The closed brane universe can be created as a result of decay of the bulk black hole.
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.
We study the behaviour of weak gravitational fields in models where a 4D brane is embedded inside a 5D brane equipped with induced gravity, which in turn is embedded in a 6D spacetime. We consider a specific regularization of the branes internal structures where the 5D brane can be considered thin with respect to the 4D one. We find exact solutions corresponding to pure tension source configurations on the thick 4D brane, and study perturbations at first order around these background solutions. To perform the perturbative analysis, we adopt a bulk-based approach and we express the equations in…
We investigate the localization of 4D topological global defects on the brane embedded in 5D. The defects are induced by 5D scalar fields with a symmetry-breaking potential. Taking an ansatz which separates the scalar field into the 4D and the extra-D part, we find that the static-hedgehog configuration is accomplished and the defects are formed only in the $AdS_4/AdS_5$ background. In the extra dimension, the localization amplitude for the 4D defects is high where the warp factor is high.
We investigate the cosmological consequences of a two brane system embedded in a higher dimensional background spacetime with a compactified extra dimension described with an action that include the intrinsic curvature for each brane. We find that the dynamics of each brane is related to the other by means of cosmological restrictions that involve the scale factors, the equation of state parameters and the Hubble parameters of the two branes. We analyze the evolution of the scale factor and the equation of state parameter for the hidden brane when in the visible brane is present a cosmological…
In the Cascading Gravity brane-world scenario, our 3-brane lies within a succession of lower-codimension branes, each with their own induced gravity term, embedded into each other in a higher-dimensional space-time. In the 6+1-dimensional version of this scenario, we show that a 3-brane with tension remains flat, at least for sufficiently small tension that the weak-field approximation is valid. The bulk solution is nowhere singular and remains in the perturbative regime everywhere.
The standard Friedmann universe embedded in a five dimensional and constant curvature bulk is examined without any a priori junction condition between the brane and the bulk. A geometrical explanation for the accelerated expansion of the universe is derived by using a minimum set of assumptions consistent with the brane-world program. It is shown that the extrinsic curvature of the brane can be associated to the dark energy which presumably drives the universe expansion.
Brane-Universe model embedded in 6-dimensional space-time with the signature (2+4) is considered. A matter is gravitationally trapped in three space dimensions, but both time-like directions are open. Choosing of the dimension and the signature of the model is initiated with the conformal symmetry for massless particles and any point in our world can be (1+1) string-like object.
A new solution to Einstein equations in (1+5)-spacetime with an embedded (1+3) brane is given. This solution localizes the zero modes of all kinds of matter fields and 4-gravity on the (1+3) brane by an increasing, transverse gravitational potential. This localization occurs despite the fact that the gravitational potential is not a decreasing exponential, and asymptotically approaches a finite value rather than zero.
This talk presents an overview of the brane cosmology scenario, based on the idea that our Universe is a 3-brane embedded in a five-dimensional anti-de Sitter bulk space-time. Special emphasis is put on the novel features of this scenario: an unconventional cosmological evolution at high energy densities, i.e. in the early universe, and dark radiation, that embodies the gravitational effects of the bulk onto the brane, and which is shown to be generated during the high energy era by the production of bulk gravitons.
These notes give an introductory review on brane cosmology. This subject deals with the cosmological behaviour of a brane-universe, i.e. a three-dimensional space, where ordinary matter is confined, embedded in a higher dimensional spacetime. In the tractable case of a five-dimensional bulk spacetime, the brane (modified) Friedmann equation is discussed in detail, and various other aspects are presented, such as cosmological perturbations, bulk scalar fields and systems with several branes.
A brane-world universe consists of a 4-dimensional brane embedded into a 5-dimensional space-time (bulk). We apply the Arnowitt-Deser-Misner decomposition to the brane-world, which results in a 3+1+1 break-up of the bulk. We present the canonical theory of brane cosmology based on this decomposition. The Hamiltonian equations allow for the study of any physical phenomena in brane gravity. This method gives new prospects for studying the initial value problem, stability analysis, brane black holes, cosmological perturbation theory and canonical quantization in brane-worlds.
The cascading gravity model was proposed to eliminate instabilities of the original DGP model by embedding our 4D universe into a 5D brane, which is itself embedded in a 6D bulk. Thus gravity cascades from 6D down to 4D as we decrease the length scales. We show that it is possible to extend this setup to lower dimensions as well, i.e. there is a self-consistent embedding of a 3D brane into a 4D brane, which is itself embedded in a 5D bulk and so on. This extension fits well into the "vanishing dimensions" framework in which dimensions open up as we increase the length scales.
In the present letter we find that Starobinsky's inflationary solution is also valid in the Dvali-Gabadadze-Porrati (DGP) model where a 3-brane is embedded in 5-dimensional Minkowski bulk. We show that such a solution is typically not supported by the Self-Accelerated branch of the model, giving therefore a natural selection of the conventional branch of solutions. In the absence of brane induced Einstein-Hilbert term the SA branch is always selected out. We then study the linearized modes around all such de Sitter brane solutions finding perturbative stability for a range of parameters of the…
