We study cosmology on a conical brane in the six-dimensional Einstein-Maxwell-dilaton system, where the extra dimensions are compactified by a magnetic flux. We systematically construct exact cosmological solutions using the fact that the system is equivalently described by (6+n)-dimensional pure Einstein-Maxwell theory via dimensional reduction. In particular, we find a power-law inflationary solution for a general dilatonic coupling. When the dilatonic coupling is given by that of Nishino-Sezgin chiral supergravity, this reduces to the known solution which is not inflating. The power-law solution is shown to be the late-time attractor. We also investigate cosmological tensor perturbations in this model using the (6+n)-dimensional description. We obtain the separable equation of motion and find that there always exist a zero mode, while tachyonic modes are absent in the spectrum. The mass spectrum of Kaluza-Klein modes is obtained numerically.
We show that brane induced gravity can be realized as a low energy effective theory of brane worlds with asymmetric warped compactification. A self-accelerating universe without cosmological constant on the brane can be realized in a model where one side of the bulk has finite volume, but the other side has infinite volume. The spin-2 perturbations for brane induced gravity and asymmetric warped compactification models have the same spectrum at low energies. For a de Sitter brane, the spin-2 graviton has mass in the range $0<m^2 \leq 2H^2$, with $m^2=2H^2$ in the self-accelerating universe.
We find a simple exact solution of 6-dimensional braneworld which captures some essential features of warped flux compactification, including a warped geometry, compactification, a magnetic flux, and one or two 3-brane(s). In this setup we analyze how the Hubble expansion rate on each brane changes when the brane tension changes. It is shown that effective Newton's constant resulting from this analysis agrees with that inferred by simply integrating extra dimensions out. Based on the result, a general formula for effective Newton's constant is conjectured and its application to cosmology with …
It is pointed out that in the warped string compactification, motion of anti-D-branes near the bottom of a throat behaves like dark matter. Several scenarios for production of the dark matter are suggested, including one based on the D/anti-D interaction at the late stage of D/anti-D inflation.
We present new exact solutions of the warped spherical compactifications in the higher-dimensional gravitational theory coupled to scalar and several form field strengths. We find two classes of solutions. One has a de Sitter spacetime with a static warp factor. The other gives an accelerating universe in the non-Einstein conformal frame with a time-dependent warp factor.
We study the cosmological evolution of extended branes in 6D warped flux compactification models. The branes are endowed with the three ordinary spatial dimensions, which are assumed to be homogeneous and isotropic, as well as an internal extra dimension compactified on a circle. We embed these codimension 1 branes in a static bulk 6D spacetime, whose geometry is a solution of 6D Einstein-Maxwell or Einstein-Maxwell-dilaton theories, corresponding to a warped flux compactification. The brane matter consists of a complex scalar field which is coupled to the bulk U(1) gauge field. In both models…
We present new solutions of warped compactifications in the higher-dimensional gravity coupled to the scalar and the form field strengths. These solutions are constructed in the D-dimensional spacetime with matter fields, with the internal space that has a finite volume. Our solutions give explicit examples where the cosmological constant or 0-form field strength leads to a de Sitter spacetime in arbitrary dimensions.
We find a cosmological solution corresponding to compactification of 10d supergravity on a warped conifold that easily circumvents `no-go' theorem given for a warped/flux compactification, providing new perspectives for the study of supergravity or superstring theory in cosmological backgrounds. With fixed volume moduli of the internal space, the model can explain a physical universe undergoing an accelerated expansion in the 4d Einstein frame, for a sufficiently long time. The solution found in the limit that the warp factor dependent on the radial coordinate $y$ is extremized (giving a const…
We consider Freund-Rubin-type compactifications which are described by (p+q)-dimensional Einstein gravity with a positive cosmological constant and a q-form flux. Using perturbative expansions of Kinoshita's ansatz for warped dS_pxS^q and AdS_pxS^q spacetimes, we obtain analytical solutions describing the warped branches and their respective phase spaces. These equations are given by inhomogeneous Gegenbauer differential equations which can be solved by the Green's function method. The requirement that the Green's functions are regular provides constraints which determine the structure of the …
We show that the warped de Sitter compactifications are possible under certain conditions in D-dimensional gravitational theory coupled to a dilaton, a form field strength, and a cosmological constant. We find that the solutions of field equations give de Sitter spacetime with the warped structure, and discuss cosmological models directly obtained from these solutions. We also construct a cosmological model in the lower-dimensional effective theory. If there is a field strength having non-vanishing components along the internal space, the moduli can be fixed at the minimum of the effective pot…
We consider the possibility of localizing gravity on a Nielsen-Olesen vortex in the context of the Abelian Higgs model. The vortex lives in a six-dimensional space-time with negative bulk cosmological constant. In this model we find a region of the parameter space leading, simultaneously, to warped compactification and to regular space-time geometry. A thin defect limit is studied. Regular solutions describing warped compactifications in the case of higher winding number are also presented.
Using DBI inflation as an example, we demonstrate that the detailed geometry of warped compactification can leave an imprint on the cosmic microwave background (CMB). We compute CMB observables for DBI inflation in a generic class of warped throats and find that the results (such as the sign of the tilt of the scalar perturbations and its running) depend sensitively on the precise shape of the warp factor. In particular, we analyze the warped deformed conifold and find that the results can differ from those of other warped geometries, even when these geometries approximate well the exact metri…
We investigate warped compactification with an abelian gauge theory in six dimensions. The vanishing cosmological constant in four dimensions can generically be realized with a regular metric even in a 3-brane background without fine tuning of couplings.
We discuss a possible compactification of a higher-dimensional gravitational theory, which give rise to a de Sitter or an accelerating universe, to the extent that it can describe a low energy limit of string theory. Such analysis can be carried out by the usual integration over the internal space in the Einstein equations. The combined field equations in the higher-dimensional supergravity theory after integration give several new terms which may help to realize a de Sitter compactification. After developing the general framework, we describe some specific examples involving the dilaton and m…
We discuss an inflation model, in which the inflation is driven by a single scalar field with exponential potential on a warped DGP brane. In contrast to the power law inflation in standard model, we find that the inflationary phase can exit spontaneously without any mechanism. The running of the index of scalar perturbation spectrum can take an enough large value to match the observation data, while other parameters are in a reasonable region.
We give a short review of a large class of warped string geometries, obtained via F-theory compactified on Calabi-Yau fourfolds, that upon reduction to 5 dimensions give consistent supersymmetric realizations of the RS compactification scenario.
In general warped compactifications, non-trivial backgrounds for the warp factor and the dilaton break $D$-dimensional diffeomorphism invariance, so that dilaton fluctuations can be gauged away completely and eaten by the metric. More specifically, the warped volume modulus and the dilaton are not independent, but combine into a single gauge-invariant degree of freedom in the lower dimensional effective theory, the warped breathing mode. This occurs for all strengths of the warping, even the weakly warped limit. This warped breathing mode appears as a natural zero mode deformation of backgroun…
An impressed feature of inflation on warped Dvali-Gabadadze-Porrati (DGP) brane is that the inflationary phase exits spontaneously for a scalar inflaton field with exponential potential, which presents a graceful exit mechanism for the inflation. But its reheating mechanism leaves open. We investigate the curvaton reheating in inflation on warped DGP brane model. The reheating may occur in effctively 5 dimensional or 4 dimensional stage. We study the permitted parameter space of the curvaton field in detail. We demonstrate how the inflation model of the warped DGP brane is improved by the curv…
Warped compactification of the six-dimensional bulk with a negative cosmological constant is realized with a 4-brane along with an abelian gauge theory. No fine tuning of couplings are needed to obtain the vanishing cosmological constant in four dimensions, as is the case for the bulk with a positive cosmological constant.
Static solutions with a bulk dilaton are derived in the context of six dimensional warped compactification. In the string frame, exponentially decreasing warp factors are identified with critical points of the low energy $β$-functions truncated at a given order in the string tension corrections. The stability of the critical points is discussed in the case of the first string tension correction. The singularity properties of the obtained solutions are analyzed and illustrative numerical examples are provided.
We give necessary conditions for the existence of perturbative heterotic and common sector type II string warped compactifications preserving four and eight supersymmetries to four spacetime dimensions, respectively. In particular, we find that the only compactifications of heterotic string with the spin connection embedded in the gauge connection and type II strings are those on Calabi-Yau manifolds with constant dilaton. We obtain similar results for compactifications to six and to two dimensions.
We discuss the spectrum of the tensor metric perturbations and the stability of warped compactifications with the de Sitter spacetime in the higher-dimensional gravity. The spacetime structure is given in terms of the warped product of the non-compact direction, the spherical internal dimensions and the four-dimensional de Sitter spacetime. To realize a finite bulk volume, we construct the brane world model, using the cut-copy-paste method. Then, we compactify the spherical directions on the brane. In any case, we show the existence of the massless zero mode and the mass gap of it with massive…
We derive four-dimensional effective theories for warped compactification of the ten-dimensional IIB supergravity. We show that these effective theories allow a much wider class of solutions than the original higher-dimensional theories. This result indicates that the effective four-dimensional theories should be used with caution, if one regards the higher-dimensional theories more fundamental.
We show that the conifold and deformed-conifold warped compactifications of the ten-dimensional type IIB supergravity, including the Klebanov-Strassler solution, are dynamically unstable in the moduli sector representing the scale of a Calabi-Yau space, although it can be practically stable for a quite long time in a region with a large warp factor. This instability is associated with complete supersymmetry breaking except for a special case and produces significant time-dependence in the structure of the four-dimensional base spacetime as well as of the internal space.
We consider warped compactifications that solve the 10 dimensional supergravity equations of motion at a point, stabilize the position of a D3-brane world, and admit a warp factor that violates Lorentz invariance along the brane. This gives a string embedding of ``asymmetrically warped'' models which we use to calculate stringy (α') corrections to standard model dispersion relations, paying attention to the maximum speeds for different particles. We find, from the dispersion relations, limits on gravitational Lorentz violation in these models, improving on current limits on the speed of gravit…
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…
The implications of brane motion in angular directions of Calabi-Yau flux compactifications are discussed from the point of view of an observer living on the worldvolume of the brane and from the point of view of an observer living elsewhere in the three non-compact dimensions. The brane observer can experience cosmological bounces and cyclic behavior of the scale factor induced by centrifugal angular momentum barriers. Observers living elsewhere in the compactification experience marginally prolonged periods of inflation due to large angular momentum (spinflation). The presence of spinflaton …
We derive four-dimensional effective theories for warped compactification of the ten-dimensional IIB supergravity and the eleven-dimensional Horava-Witten model. We show that these effective theories allow a much wider class of solutions than the original higher-dimensional theories. In particular, the effective theories have cosmological solutions in which the size of the internal space decreases with the cosmic expansion in the Einstein frame. This type of compactifying solutions are not allowed in the original higher-dimensional theories. This result indicates that the effective four-dimens…
Warped string compactifications, characterized by non-singular behavior of the metric in the infrared (IR), feature departures from the usual anti-de Sitter warped extra dimensions. We study the implications of the smooth IR cutoff for Randall-Sundrum (RS) type models. We find that the phenomenology of the KK gravitons (including their masses and couplings) depends sensitively on the precise shape of the warp factor in the IR. In particular, we analyze the warped deformed conifold and find that the spectrum differs significantly from that of RS, and present a simple prescription (a mass gap an…
We construct the effective theory of the universal Kaehler modulus in warped compactifications using the Hamiltonian formulation of general relativity. The spacetime dependent 10d solution is constructed at the linear level for both the volume modulus and its axionic partner, and nontrivial cancellations of warping effects are found in the dimensional reduction. Our main result is that the Kaehler potential is not corrected by warping, up to an overall shift in the background value of the volume modulus. We extend the analysis beyond the linearized approximation by computing the fully backreac…
We continue our study of codimension two solutions of warped space-time varying compactifications of string theory. In this letter we discuss a non-supersymmetric solution of the classical type IIB string theory with de Sitter gravity on a codimension two uncompactified part of spacetime. A non-zero positive value of the cosmological constant is induced by the presence of non-trivial stringy moduli, such as the axion-dilaton system for the type IIB string theory. Furthermore, the naked singularity of the codimension two solution is resolved by the presence of a small but non-zero cosmological …
In this paper, we discuss the time-dependent brane solutions in higher-dimensional supergravity theories. We particularly focus on the dynamical extensions of the intersecting brane solutions involving three branes. We also show that in the near-horizon limits, where the time dependence is negligible, these branes describe warped anti-de Sitter spacetimes as in the corresponding static solutions. We finally examine the lower-dimensional cosmological dynamics obtained after compactifications of the higher-dimensional solutions and show the solutions we have found give the four-dimensional unive…
The moduli space of N=1 type II warped compactions to flat space with generic internal fluxes is studied. Using the underlying integrable generalized complex structure that characterizes these vacua, the different deformations are classified by H-twisted generalized cohomologies and identified with chiral and linear multiplets of the effective four-dimensional theory. The Kaehler potential for chiral fields corresponding to classically flat moduli is discussed. As an application of the general results, type IIB warped Calabi-Yau compactifications and other SU(3)-structure subcases are consider…
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…
Orientifolds with three-form flux provide some of the simplest string examples of warped compactification. In this paper we show that some models of this type have the unusual feature of D=4, N=3 spacetime supersymmetry. We discuss their construction and low energy physics. Although the local form of the moduli space is fully determined by supersymmetry, to find its global form requires a careful study of the BPS spectrum.
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 explore the generic motion of cosmic (super)strings when the internal compact dimensions are warped, using the Klebanov-Strassler solution as a prototypical throat geometry. We find that there is no dynamical mechanism which localises the string at the tip of the throat, but rather that the motion seems to explore both internal and external degrees of freedom democratically. This indicates that cosmic (super)strings formed by inflationary brane-antibrane annihilation will have sufficient internal motion for the gravitational wave signals from the string network to be suppressed relative to …
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 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…
We present a systematic way to derive the four-dimensional effective theories for warped compactifications with fluxes and branes in the ten-dimensional type IIB supergravity. The ten-dimensional equations of motion are solved using the gradient expansion method and the effective four-dimensional equations of motions are derived by imposing the consistency condition that the total derivative terms with respect to the six-dimensional internal coordinates vanish when integrated over the internal manifold. By solving the effective four-dimensional equations, we can find the gravitational backreac…
We study M and F theory compactifications on Calabi-Yau four-folds in the presence of non-trivial background flux. The geometry is warped and belongs to the class of p-brane metrics. We solve for the explicit warp factor in the orbifold limit of these compactifications, compare our results to some of the more familiar recently studied warped scenarios, and discuss the effects on the low-energy theory. As the warp factor is generated solely by backreaction, we may use topological arguments to determine the massless spectrum. We perform the computation for the case where the four-fold equals K3 …
We explore in detail the prospects of obtaining a four-dimensional de Sitter universe in classical supergravity models with warped and time-independent extra dimensions, presenting explicit cosmological solutions of the $(4+n)$-dimensional Einstein equations with and without a bulk cosmological constant term. For the first time in the literature we show that there may exist a large class of warped supergravity models with a noncompact extra dimension which lead to a finite 4D Newton constant as well as a massless 4D graviton localised on an inflating four-dimensional FLRW universe. This result…
We propose a cosmological model which exhibits the phenomenon of self-acceleration: the Universe is attracted to the phase of accelerated expansion at late times even in the absence of the cosmological constant. The self-acceleration is inevitable in the sense that it cannot be neutralized by any negative explicit cosmological constant. The model is formulated in the framework of brane-world theories with a warped extra dimension. The key ingredient of the model is the brane-bulk energy transfer which is carried by bulk vector fields with a sigma-model-like boundary condition on the brane. We …
We study the regularization of the codimension-2 singularities in six-dimensional Einstein-Maxwell axisymmetric models with warping. These singularities are replaced by codimension-1 branes of a ring form, situated around the axis of symmetry. We assume that there is a brane scalar field with Goldstone dynamics, which is known to generate a brane energy momentum tensor of a particular structure necessary for the above regularization to be successful. We study these compactifications in both a non-supersymmetric and a supersymmetric setting. We see that in the non-supersymmetric case, there is …
We review warped compactifications of superstring theory with some attention to the limit in which these resemble "bottom-up" phenomenological models. In addition to some discussion of the original Klebanov-Witten and Klebanov-Strassler set-ups, we also touch on various generalizations of the geometry that have been considered. Various other systems with a holographic duality are also briefly reviewed. The point of this latter exploration is to illustrate how far beyond the standard AdS(5) x S(5) set-up things have moved over the years.
The recent PAMELA and ATIC/Fermi/HESS experiments have observed an excess of electrons and positrons, but not anti-protons, in the high energy cosmic rays. To explain this result, we construct a decaying hidden dark matter model in string theory compactification that incorporates the following two ingredients, the hidden dark matter scenario in warped compactification and the phenomenological proposal of hidden light particles that decay to the Standard Model. In this model, on higher dimensional warped branes, various warped Kaluza-Klein particles and the zero-mode of gauge field play roles o…
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,…
In asymmetrically warped spacetimes different warp factors are assigned to space and to time. We discuss causality properties of these warped brane universes and argue that scenarios with two extra dimensions may allow for timelike curves which can be closed via paths in the extra-dimensional bulk. In particular, necessary and sufficient conditions on the metric for the existence of closed timelike curves are presented. We find a six-dimensional warped metric which satisfies the CTC conditions, and where the null, weak and dominant energy conditions are satisfied on the brane (although only th…
The dynamics of warped/flux compactifications is studied, including warping effects, providing a firmer footing for investigation of the "landscape." We present a general formula for the four-dimensional potential of warped compactifications in terms of ten-dimensional quantities. This allows a systematic investigation of moduli-fixing effects and potentials for mobile branes. We provide a necessary criterion, "slope-dominance," for evading "no-go" results for de Sitter vacua. We outline the ten-dimensional derivation of the non-perturbative effects that should accomplish this in KKLT examples…
We discuss Casimir effect of a massless, minimally coupled scalar field in a 6D warped flux compactification model and its implications for the hierarchy and cosmological constant problems, which are longstanding puzzles in phenomenology and cosmology. Due to the scale invariance of the background theory, the 4D effective theory contains a volume modulus. To stabilize the modulus, we consider one-loop corrections to the effective potential by the Casimir effect. The one-loop effective potential for the volume modulus has a form which is very similar to Coleman-Weinberg potential. We evaluate c…
We deal with scalar field coupled to gravity in five dimensions in warped geometry. We investigate models described by potentials that drive the system to support thick brane solutions that engender internal structure. We find analytical expressions for the brane solutions, and we show that they are all linearly stable.
It has been suggested that the observed value of the cosmological constant is related to the supersymmetry breaking scale M_{susy} through the formula Lambda \sim M_p^4 (M_{susy}/M_p)^8. We point out that a similar relation naturally arises in the codimension two solutions of warped space-time varying compactifications of string theory in which non-isotropic stringy moduli induce a small but positive cosmological constant.
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…
We analyze the wavefunctions for open strings stretching between intersecting 7-branes in type IIB/F-theory warped compactifications, as a first step in understanding the warped effective field theory of 4d chiral fermions. While in general the equations of motion do not seem to admit a simple analytic solution, we provide a method for solving the wavefunctions in the case of weak warping. The method describes warped zero modes as a perturbative expansion in the unwarped spectrum, the coefficients of the expansion depending on the warping. We perform our analysis with and without the presence …
We investigate aspects of the four-dimensional effective description of brane world scenarios based on warped compactification on anti-de Sitter space. The low-energy dynamics is described by visible matter gravitationally coupled to a ``dark'' conformal field theory. We give the linearized description of the 4d stress tensor corresponding to an arbitrary 5d matter distribution. In particular a 5d falling particle corresponds to a 4d expanding shell, giving a 4d interpretation of a trajectory that misses a black hole only by moving in the fifth dimension. Breakdown of the effective description…
In this paper, we compute the massive modes of scalar and gauge fields in a multiply warped brane-world scenario in six-dimensional spacetime with a Freedman-Robertson-Walker (FRW) metric. The massive Kaluza-Klein (KK) modes of the fields are split in two mass towers due to the presence of the warped in both dimensions. This does not occurs in the standard Randall-Sundrum (RS) model. We investigate the dependence of the mass spectrum on Hubble constant. Lighter massive modes of the fields are found, whereby it is possible to infer that scalar and bosonic matter can directly influence in univer…
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 analyze observational constraints on the parameter space of tachyonic inflation with a Gaussian potential and discuss some predictions of this scenario. As was shown by Kofman and Linde, it is extremely problematic to achieve the required range of parameters in conventional string compactifications. We investigate if the situation can be improved in more general compactifications with a warped metric and varying dilaton. The simplest examples are the warped throat geometries that arise in the vicinity of of a large number of space-filling D-branes. We find that the parameter range for infla…
We study gravitational waves propagating on a warped Minkowski space-time with D-4 compact extra dimensions. While Kaluza-Klein scales are typically too high for any current detection, we analyse how the warp factor changes the Kaluza-Klein spectrum of gravitational waves. To that end we provide a complete and explicit expression for the warp factor, as well as the Green's function, on a d-dimensional torus. This expression differs from that of braneworld models and should find further uses in string compactifications. We then evaluate the Kaluza-Klein spectrum of gravitational waves. Our prel…
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 study the cosmology induced on a brane probing a warped throat region in a Calabi-Yau compactification of type IIB string theory. For the case of a BPS D3-brane probing the Klebanov-Strassler warped deformed conifold, the cosmology described by a suitable brane observer is a bouncing, spatially flat Friedmann-Robertson-Walker universe with time-varying Newton's constant, which passes smoothly from a contracting to an expanding phase. In the Klebanov-Tseytlin approximation to the Klebanov-Strassler solution the cosmology would end with a big crunch singularity. In this sense, the warped defo…
