We show how to define a consistent braneworld cosmology in a model in which the brane is constructed as a field-theoretic domain wall of finite thickness. The Friedmann, Robertson-Walker metric is recovered in the region of the brane, but, remarkably, with scale factor that depends on particle energy and on particle species, constituting a breakdown of the weak equivalence principle on sufficiently small scales. This unusual effect comes from the extended nature of particles confined to a domain-wall brane, and the fact that they feel an "average" of the bulk spacetime. We demonstrate how to recover the standard results of brane cosmology in the infinitely-thin brane limit, and comment on how our results have the potential to place bounds on parameters such as the thickness of domain-wall braneworlds.
The brane cosmology has invoked new challenges to the usual Big Bang cosmology. In this paper we present a brief account on thermal history of the post-inflationary brane cosmology. We have realized that it is not obvious that the post-inflationary brane cosmology would always deviate from the standard Big Bang cosmology. However, if it deviates some stringent conditions on the brane tension are to be satisfied. In this regard we study various implications on gravitino production and its abundance. We discuss Affleck-Dine mechanism for baryogenesis and make some comments on moduli and dilaton …
We discuss cosmology in four dimensions within a context of brane-world scenario.Such models can predict chaotic inflation with very low reheat temperature depending on the brane tension. We notice that the gravitino abundance is different in the brane-world cosmology and by tuning the brane tension it is possible to get extremely low abundance. We also study Affleck-Dine baryogenesis in our toy model.
We consider ``brane-universes'', where matter is confined to four-dimensional hypersurfaces (three-branes) whereas one extra compact dimension is felt by gravity only. We show that the cosmology of such branes is definitely different from standard cosmology and identify the reasons behind this difference. We give a new class of exact solutions with a constant five-dimensional radius and cosmologically evolving brane. We discuss various consequences.
We discuss D-braneworld cosmology, that is, the brane is described by the Born-Infeld action. Compared with the usual Randall-Sundrum braneworld cosmology where the brane action is the Nambu-Goto one, we can see some drastic changes at the very early universe: (i)universe may experience the rapid accelerating phase (ii)the closed universe may avoid the initial singularity. We also briefly address the dynamics of the cosmology in the open string metric, which might be favorer than the induced metric from the view point of the D-brane.
We study cosmology in a five-dimensional brane-world with a stabilizing effective potential for the radion and matter localized on the two branes. We consider the corrections induced by the Gauss-Bonnet contribution to the total action performing and expansion around the two possible static solutions up to second order in the ratio between brane matter energy density and brane tensions. The Friedmann and acceleration equations on the visible brane are obtained and discussed.
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.
Recent theoretical developments have generated a strong interest in the ``brane-world'' picture, which assumes that ordinary matter is trapped in a three-dimensional submanifold, usually called brane, embedded in a higher dimensional space. The purpose of this review is to introduce some basic results concerning gravity in these models and then to present various aspects of the cosmology in a brane-universe.
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…
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 five dimensional brane cosmology with non-minimally coupled scalar field to gravity has been considered in a Jordan-Brans-Dicke frame. We derive an effective four dimensional field equations on a 3+1 dimensional brane where the fifth dimension has been assumed to have an orbifold symmetry. We have noticed that the evolution equation for the matter component stuck to the brane is non-trivially coupled to the scalar field living on the brane and the bulk. Finally we discuss some cosmological consequences of this set-up.
We consider the effect of string inhomogeneities on the time dependent background of Brane Gas Cosmology. We derive the equations governing the linear perturbations of the dilaton-gravity background in the presence of string matter sources. We focus on long wavelength fluctuations and find that there are no instabilities. Thus, the predictions of Brane Gas Cosmology are robust against the introduction of linear perturbations. In particular, we find that the stabilization of the extra dimensions (moduli) remains valid in the presence of dilaton and string perturbations.
We investigate aspects of cosmology in brane world theories with a bulk scalar field. We concentrate on a recent model motivated from supergravity in singular spaces. After discussing the background evolution of such a brane-world, we present the evolution of the density contrast. We compare our results to those obtained in the (second) Randall-Sundrum scenario and usual 4D scalar-tensor theories.
We consider the effect of the ultraviolet (UV) or short wavelength modes on the background of Brane Gas Cosmology. We find that the string matter sources are negligible in the UV and that the evolution is given primarily by the dilaton perturbation. We also find that the linear perturbations are well behaved and the predictions of Brane Gas Cosmology are robust against the introduction of linear perturbations. In particular, we find that the stabilization of the extra dimensions (moduli) remains valid in the presence of dilaton and string perturbations.
We study cosmological solutions in the dilatonic brane world models. The effective four-dimensional equations on the brane are analyzed for the models with one positive tension brane and two branes with tensions of opposite signs. Just as in the non-dilatonic brane case, the conventional Friedmann equations of the four-dimensional universe are reproduced to the leading order in matter energy density for the model with one brane and the introduction of a radion potential is required in order to reproduce the Friedmann equations with the correct sign for the model with two branes.
We study cosmology in the five-dimensional Randall-Sundrum brane-world with a stabilizing effective potential for the radion and matter localized on the branes. The analysis is performed by employing a perturbative expansion in the ratio rho/V between the matter energy density on the branes and the brane tensions around the static Randall-Sundrum solution (which has rho=0 and brane tensions +-V). This approach ensures that the matter evolves adiabatically and allows us to find approximate solutions to second order in ρ/V. Some particular cases are then analyzed in details.
We consider ``cosmologically symmetric'' (i.e. solutions with homogeneity and isotropy along three spatial dimensions) five-dimensional spacetimes with a scalar field and a three-brane representing our universe. We write Einstein's equations in a conformal gauge, using light-cone coordinates. We obtain explicit solutions: a. assuming proportionality between the scalar field and the logarithm of the (bulk) scale factor; b. assuming separable solutions. We then discuss the cosmology in the brane nduced by these solutions.
This contribution presents the cosmological models with extra dimensions that have been recently elaborated, which assume that ordinary matter is confined on a surface, called brane, embedded in a higher dimensional spacetime.
We investigate braneworld cosmology based on the D-brane initiated in our previous paper. The brane is described by a Born-Infeld action and the gauge field is contained. The higher order corrections of an inverse string tension will be addressed. The results obtained by the truncated argument are altered by the higher order corrections. The equation of state of the gauge field on the brane is radiation-like in low energy scales and almost dust-like fluid in high energy scales. Our model is, however, limited below a critical finite value of the energy density. For the description of full histo…
We derive the Friedmann-like equations in braneworld cosmology by imposing the first law of thermodynamics and Bekenstein's area-entropy formula on the apparent horizon of a Friedmann-Roberston-Walker universe in both Randall-Sundrum II gravity and Dvali-Gabadadze-Porrati gravity models. Israel's boundary condition plays an important role in our calculations in both cases, besides the first law of thermodynamics and Bekenstein's area-entropy formula. The results indicate that thermodynamics on the brane world knows the behaviors of gravity.
In this paper we consider some constraints on brane-world cosmologies. In the first part we analyze different behaviors for the expansion of our universe by imposing constraints on the speed of sound. In the second part, we study the nature of matter on the brane world by means of the well-known energy conditions. We find that the strong energy condition must be completely violated at late stages of the universe.
The cosmology of branes undergoing the self-tuning mechanism of the cosmological constant is considered. The equations and matching conditions are derived in several coordinate systems, and an exploration of possible solution strategies is performed. The ensuing equations are solved analytically in the probe brane limit. We classify the distinct behavior for the brane cosmology and we correlate them with properties of the bulk (static) solutions. Their matching to the actual universe cosmology is addressed.
A brief review of the field of braneworld cosmology, from its inception with the large extra dimension scenario, to aspects of cosmology in warped extra dimensions, including the RS-I and RS-II models, braneworld inflation, the Goldberger-Wise mechanism, mirage cosmology, the radion-induced phase transition in RS-I, possible gravity wave signals, and the DGP model.
We consider cosmological two-brane models with AdS bulk, for which the radion, i.e. the separation between the two branes, is time dependent. In the case of two de Sitter branes (including Minkowski branes as a limiting case), we compute explicitly, without any approximation, the effective four-dimensional action for the radion. With the scale factor on-shell, this provides the non-perturbative dynamics for the radion. We discuss the differences between the dynamics derived from the four-dimensional action with the scale factor off-shell and the true five-dimensional dynamics.
D-branes are fundamental in all scenarios where there are large extra dimensions and the string scale is much smaller than the four-dimensional Planck mass. We show that this current picture leads to a new approach to string cosmology where inflation on our brane is driven by the large extra dimensions and the issue of the graceful exit becomes inextricably linked to the problem of the stabilization of the extra dimensions, suggesting the possibility of a common solution. We also show that branes may violently fluctuate along their transverse directions in curved spacetime, possibly leading to…
Brane Gas Cosmology (BGC) is an approach to unifying string theory and cosmology in which matter is described by a gas of strings and branes in a dilaton gravity background. The Universe is assumed to start out with all spatial dimensions compact and small. It has previously been shown that in this context, in the approximation of neglecting inhomogeneities and anisotropies, there is a dynamical mechanism which allows only three spatial dimensions to become large. However, previous studies do not lead to any conclusions concerning the isotropy or anisotropy of these three large spatial dimensi…
Using the thin-shell formalism we discuss the motion of domain walls in de Sitter and anti-de Sitter (AdS) time-dependent bulks. This motion results in a dynamics for the brane scale factor. We show that in the case of a clean brane the scale factor describes both singular and non-singular universes, with phases of contraction and expansion. These phases can be understood as quotients of AdS spacetime by a discrete symmetry group. We discuss this effect in some detail, and suggest how the AdS/CFT correspondence could be applied to obtain a non perturbative description of brane-world string cos…
We consider the homogeneous cosmological radion, which we define as the interbrane distance in a two brane and $Z_2$ symmetrical configuration. In a coordinate system where one of the brane is at rest, the junction conditions for the second (moving) brane give directly the (non-linear) equations of motion for the radion. We analyse the radion fluctuations and solve the non-linear dynamics in some simple cases of interest.
Traditionally, higher-dimensional cosmological models have sought to provide a description of the fundamental forces in terms of a unifying geometrical construction. In this essay we discuss how, in their present incarnation, higher-dimensional `braneworld' models might provide answers to a number of cosmological puzzles including the issue of dark energy and the nature of the big-bang singularity.
We derive exact solutions of the Einstein equations in the context of the Randall-Sundrum model with matter both on the brane and in the bulk. The bulk metric is a generalization of the static metrics describing the interior of stellar objects. We study the cosmological evolution on the brane. Our solutions describe energy ouflow from the brane, and the appearance of ``mirage'' contributions to the Hubble expansion that alter the standard cosmological evolution.
The possibility to study the M/string theory cosmology via 5d bulk & brane action is investigated. The role of the 4-form field in the theory of BPS branes in 5d is clarified. We describe arguments suggesting that the effective 4d description of the universe in the ekpyrotic scenario (hep-th/0103239) should lead to contraction rather than expansion of the universe. To verify these arguments, we study the full 5d action prior to its integration over the 5th dimension. We show that if one adds the potential V(Y) to the action of the bulk brane, then the metric ansatz used in the ekpyrotic scenar…
Partial reduction is a Randall-Sundrum reduction for only part of the AdS region between finite tension brane and zero tension brane. This is interesting in AdS/BCFT where the AdS bulk contains a defect brane. We employ partial reduction for a AdS bulk with a brane evolving as a $2d$ Friedmann-Robertson-Walker (FRW) cosmology and demonstrate the equivalence between defect extremal surface and island formula for a large subregion fine grained entropy in boundary CFT. We then move to higher dimensions and demonstrate the existence of $4d$ massless graviton on AdS$_4$ brane in partial reduction. …
In this paper a general solution is found for a five dimensional orbifold spacetime that induces a $k=0$ cosmology on a three-brane. Expressions for the energy density and pressure on the brane in terms of the brane metric are derived. Given a metric on the brane it is possible to find five dimensional spacetimes that contain the brane. This calculation is carried out for an inflationary universe and for a metric that corresponds to a radiation dominated universe in standard cosmology. It is also shown that any $k=0$ cosmology can be embedded in a flat five dimensional orbifold spacetime and t…
We introduce a duality relation between two distinct branes, a cosmological brane with macroscopic matter and a holographic brane with microscopic gauge fields. Using brane-world cosmology with a single brane in a 5-dimensional AdS5 background, we find an explicit time-dependent holographic correspondence between the bulk metric surrounding the cosmological brane and the N=4 gauge field theory living on the boundary of the Z2-symmetric mirror bulk, identified with the holographic brane. We then relate the cosmic acceleration on the cosmological brane to the conformal anomaly of the gauge theor…
The brane-world cosmological model in higher-dimensional spacetime with a bulk scalar field is investigated. We derive the $(4+n)$-dimensional gravitational field equations for the scalar field on the $(3+n)$-brane in a $(5+n)$-dimensional bulk with Einstein gravity plus a self-interacting scalar field. The $(4+n)$-dimensional gravitational field equations can be formulated to standard form with the extra component. Using this formalism we study the Kaluza-Klein brane cosmology. We derive the Friedmann equation and a possible energy leak out of the brane into the bulk. We present some exact so…
In the study of three-brane cosmological models, an unusual law of cosmological expansion on the brane has been reported. According to this law, the energy density of matter on the brane quadratically enters the right-hand side of the new equations for the brane world, in contrast with the standard cosmology, where it enters the similar equations linearly. However, this result is obtained in the absence of curvature-dependent terms in the action for the brane. In this paper, we derive the field equations for a brane world embedded into a five-dimensional spacetime in the case where such terms …
An overview is presented of some cosmological aspects of string theory. Recent developments are emphasised, especially the attempts to derive inflation or alternatives to inflation from the dynamics of branes in string theory. Time dependent backgrounds with potential cosmological implications, such as those provided by negative tension branes and S-branes and the rolling string tachyon are also discussed.
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 cosmology of models with four space and one time dimension where our universe is a 3-brane and report a few results which extend existing work in several directions. Assuming a stable fifth dimension, we obtain a solution for the metric, which does not depend on any arbitrary parameters. We discuss some implications of this result.
We compute the holographic quark potential in the realm of brane cosmology. We show that under certain conditions the very geometry due to an inflationary 3-brane induces a D3-D7-brane system. The cosmological constant that appears involved in the original geometry is attributed to the D7-brane position itself in its embedding process. We address the issues of confinement at low distances, screening effects at sufficiently large distances, and quark condensate.
We consider the cosmological evolution of a brane in the presence of a bulk scalar field coupled to the Ricci scalar through a term f(ϕ)R. We derive the generalized Friedmann equation on the brane in the presence of arbitrary brane and bulk-matter, as well as the scalar field equation, allowing for a general scalar potential V(phi). We focus on a quadratic form of the above non-minimal coupling and obtain a class of late-time solutions for the scale factor and the scalar field on the brane that exhibit accelerated expansion for a range of the non-minimal coupling parameter.
We explore various facets of the cosmology of the Randall-Sundrum scenario with two branes by considering the dynamics of the branes moving in a bulk AdS/Schwarzschild geometry. This approach allows us both to understand in more detail and from a different perspective the role of the stabilization of the hierarchy in the brane cosmology, as well as to extend to the situation where the metric contains a horizon. In particular, we explicitly determine how the Goldberger-Wise stabilization mechanism perturbs the background bulk geometry to produce a realistic cosmology.
In the context of an inflationary Randall-Sundrum Type II braneworld (RS2) we calculate spectral indices and amplitudes of cosmological scalar and tensor perturbations, up to second order in slow-roll parameters. Under very simple assumptions, extrapolating next-order formulae from first-order calculations in the case of a de Sitter brane, we see that the degeneracy between standard and braneworld lowest-order consistency equations is broken, thus giving different signatures of early-universe inflationary expansion. Using the latest results from WMAP for estimates of cosmological observables, …
We consider a brane generated by a scalar field domain wall configuration in 4+1 dimensions, interpolating, in most cases, between two vacua of the field. We study the cosmology of such a system in the cases where the effective four-dimensional brane metric is de Sitter or anti de Sitter, including a discussion of the bulk coordinate singularities present in the de-Sitter case. We demonstrate that a scalar field kink configuration can support a brane with dS$_4$ cosmology, despite the presence of coordinate singularities in the metric. We examine the trapping of fermion fields on the domain wa…
We derive a new class of time-dependent solutions for the Randall-Sundrum model by patching together isometries broken by the brane. Solutions generated by generalized boosts along the fifth dimension are associated with localized gravity and lead to an effective Friedman equation on the brane with a scale factor exhibiting power law or exponential behaviour. The effective energy-density on the brane depends linearly on the brane tension.
In the context of homogeneous and isotropic superstring cosmology, the T-duality symmetry of string theory has been used to argue that for a background space-time described by dilaton gravity with strings as matter sources, the cosmological evolution of the Universe will be nonsingular. In this Letter we discuss how T-duality extends to brane gas cosmology, an approximation in which the background space-time is again described by dilaton gravity with a gas of branes as a matter source. We conclude that the arguments for nonsingular cosmological evolution remain valid.
In the context of brane gas cosmology in superstring theory, we show why it is impossible to simultaneously stabilize the dilaton and the radion with a general gas of strings (including massless modes) and D-branes. Although this requires invoking a different mechanism to stabilize these moduli fields, we find that the brane gas can still play a crucial role in the early universe in assisting moduli stabilization. We show that a modest energy density of specific types of brane gas can solve the overshoot problem that typically afflicts potentials arising from gaugino condensation.
We investigate the thermal relic density of the cold dark matter in the context of the brane world cosmology. Since the expansion law in a high energy regime is modified from the one in the standard cosmology, if the dark matter decouples in such a high energy regime its relic number density is affected by this modified expansion law. We derive analytic formulas for the number density of the dark matter. It is found that the resultant relic density is characterized by the ``transition temperature'' at which the modified expansion law in the brane world cosmology is connecting with the standard…
The thermal relic density of the neutralino dark matter in the brane world cosmology is studied. Since the expansion law at a high energy regime in the brane world cosmology is modified from the one in the standard cosmology, the resultant relic density can be altered. It has been found that, if the five dimensional Planck mass $M_5$ is lower than $10^4$ TeV, the brane world cosmological effect is significant at the decoupling time and the resultant relic density is enhanced. We calculate the neutralino relic density in the Constrained Minimal Supersymmetric Standard Model (CMSSM) and show tha…
In light of the recent Planck 2015 results for the measurement of the CMB anisotropy, we study simple inflationary models in the context of the Gauss-Bonnet brane-world cosmology. The brane-world cosmological effect modifies the power spectra of scalar and tensor perturbations generated by inflation and causes a dramatic change for the inflationary predictions of the spectral index ($n_s$) and the tensor-to-scalar ratio ($r$) from those obtained in the standard cosmology. In particular, the power spectrum of tensor perturbation is suppressed due to the Gauss-Bonnet brane-world cosmological eff…
The thermal leptogenesis in brane world cosmology is studied. In brane world cosmology, the expansion law is modified from the four-dimensional standard cosmological one at high temperature regime in the early universe. As a result, the well-known upper bound on the lightest light neutrino mass induced by the condition for the out-of-equilibrium decay of the lightest heavy neutrino, $\tilde{m}_1 \lesssim 10^{-3}$ eV, can be moderated to be $\tilde{m}_1 \lesssim 10^{-3} {eV} \times (M_1/T_t)^2 $ in the case of $T_t \leq M_1$ with the lightest heavy neutrino mass ($M_1$) and the ``transition tem…
We discuss a brane based inflationary scenario in which an initially non-supersymmetric configuration involving a D4 brane is dynamically transformed into a supersymmteric one in a background space-time geometry determined by a stack of D6 branes. Inflation is realized in the effective four dimensional theory and ends after reaching a stable BPS configuration. The scalar spectral index turns out to be 0.98. Under some simplifying assumption the reheat temperature, Hubble constant and the string scale are estimated to be of order $10^{8}$ GeV, $10^{12}$ GeV and $10^{16}$ GeV, respectively.
Gravitational particle production in time variable metric of an expanding universe is efficient only when the Hubble parameter $H$ is not too small in comparison with the particle mass. In standard cosmology, the huge value of the Planck mass $M_{Pl}$ makes the mechanism phenomenologically irrelevant. On the other hand, in braneworld cosmology the expansion rate of the early universe can be much faster and many weakly interacting particles can be abundantly created. Cosmological implications are discussed.
Modifications to the Friedmann equation in brane cosmology can have important implications for early universe phenomena such as inflation and the generation of the baryon asymmetry. In the framework of braneworld cosmology, we discuss a mechanism for baryogenesis via leptogenesis in the supersymmetric context, where the sneutrino is responsible for both inflation and the generation of the baryon asymmetry in the universe.
The gravitino dark matter hypothesis in the brane cosmology is studied. The theoretical framework is the CMSSM for particle physics and RS II brane model for gravity. It is found that the gravitino can play the role of dark matter in the universe and we determine what the gravitino mass should be for different values of the five-dimensional Planck mass. An upper bound is obtained for the latter.
We study axion cosmology in a 5D Universe, in the case of flat and warped extra dimension. The comparison between theoretical predictions and observations constrains the 5D axion decay constant and the 5D Planck mass, which has to be taken into account in building 5D axion models. The framework developed in this paper can be readily applied to other bulk fields in brane universes.
We discuss dark matter in the brane world scenario. We work in the Randall-Sundrum type II brane world and assume that the lightest supersymmetric particle is the axino. We find that the axinos can play the role of cold dark matter in the universe, provided that the five-dimensional Planck mass is bounded both from below and from above. This is possible for higher reheating temperatures compared to the conventional four-dimensional cosmology due to a novel expansion law for the universe.
We consider hybrid inflation in the braneworld scenario. In particular, we consider inflation in global supersymmetry with the D-terms in the scalar potential for the inflaton field to be the dominant ones (D-term inflation). We find that D-term dominated inflation can naturally accomodate all requirements of the successful hybrid inflationary model also in the framework of D-brane cosmology with global supersymmetry. The reheating temperature after inflation can be high enough ($\sim 10^{10} GeV$) for successful thermal leptogenesis.
The gravitational equations of the 5-dimensional analogue of the AdSS space-time, where all the matter fields are confined on the 3-brane are examined. The most general solutions are established in the generic case of a non-Z_2-symmetric bulk. Constraining these solutions we derive a number of remarkable metrics widely investigated in the literature. Finally, we make many important conclusions about the viability of the presented scenario and cosmology.
We analyze the dark matter problem in the context of brane cosmology. We investigate the impact of the non-conventional brane cosmology on the relic abundance of non-relativistic stable particles in high and low reheating scenarios. We show that in case of high reheating temperature, the brane cosmology may enhance the dark matter relic density by many order of magnitudes and a stringent lower bound on the five dimensional scale is obtained. We also consider low reheating temperature scenarios with chemical equilibrium and non-equilibrium. We emphasize that in non-equilibrium case, the resulti…
