一个4+1维宇宙模型

我们讨论的4+1维宇宙模型是通常的四维时空和一个紧致的一维内禀空间的直积空间。我们假定四维时空的能量密度是以辐射为主的,而内禀子空间的能动张量是一个阶跃函数。通过求解五维的Einstein场方程得到前四维时空由de-Sitter解过渡到标准模型的辐射为主解,与此同时内禀子空间的尺度由减幅振荡过渡到为按t的负幂次收缩而趋于一常量。 关键词：     

Scale-dependent three-dimensional charged black holes in linear and non-linear electrodynamics

In the present work we study the scale dependence at the level of the effective action of charged black holes in Einstein–Maxwell as well as in Einstein–power-Maxwell theories in \((2+1)\)-dimensional spacetimes without a cosmological constant. We allow for scale dependence of the gravitational and electromagnetic couplings, and we solve the corresponding generalized field equations imposing the null energy condition. Certain properties, such as horizon structure and thermodynamics, are discussed in detail.     

Minimal immersions,Einstein's equations and Mach's principle

A geometrical stress energy tensor for semi-Riemannian manifolds is described and a Mach's principle is formulated. It is shown that vacuum occurs if and only if the manifold is a totally geodesic submanifold of a flat semi-Euclidean space. Furthermore the Einstein equations are attained with the cosmological constant appearing as the mean curvature of an isometric immersion. A minimal submanifold of a semi-Euclidean space can thereby be regarded as a solution to Einsteins equations without a cosmological constant. Intrinsic conditions that will allow a 4-dimensional semi-Riemannian manifold to be immersed isometrically into 5-dimensional semi-Euclidean space as a minimal hypersurface are found. From this result it is possible to find explicit minimal hypersurfaces of Robertson-Walker type in a 5-dimensional Minkowski space and it is observed that they all contain an initial singularity.     

Five-Dimensional Warped Product Space-Time with Time-Dependent Warp Factor and Cosmology of the Four-Dimensional Universe

In this paper, we have studied a 5-dimensional warped product space-time with a time-dependent warp factor. This warp factor plays an important role in localizing matter to the 4-dimensional hypersurface constituting the observed universe and leads to a geometric interpretation of dynamical dark energy. The five-dimensional field equations are constructed and its solutions are obtained. The nature of modifications produced by this warp factor in the bulk geometry is discussed. The hypersurface is described by a flat FRW-type metric in the ordinary spatial dimension. It is found that the effective cosmological constant of the four-dimensional universe is a variable quantity monitored by the time-dependent warp factor. The universe is initially decelerated, but subsequently makes a transition to an accelerated phase at later times.     

Dark energy and gravity

I review the problem of dark energy focussing on cosmological constant as the candidate and discuss what it tells us regarding the nature of gravity. Section 1 briefly overviews the currently popular “concordance cosmology” and summarizes the evidence for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as a candidate and emphasizes why no other approach really solves the conceptual problems usually attributed to cosmological constant. Section 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract certain key ingredients which must be present in any viable solution. In the conventional approach, the equations of motion for matter fields are invariant under the shift of the matter Lagrangian by a constant while gravity breaks this symmetry. I argue that until the gravity is made to respect this symmetry, one cannot obtain a satisfactory solution to the cosmological constant problem. Hence cosmological constant problem essentially has to do with our understanding of the nature of gravity. Section 3 discusses such an alternative perspective on gravity in which the gravitational interaction—described in terms of a metric on a smooth spacetime—is an emergent, long wavelength phenomenon, and can be described in terms of an effective theory using an action associated with normalized vectors in the spacetime. This action is explicitly invariant under the shift of the matter energy momentum tensor T _ab → T _ab + Λ _gab and any bulk cosmological constant can be gauged away. Extremizing this action leads to an equation determining the background geometry which gives Einstein’s theory at the lowest order with Lanczos–Lovelock type corrections. In this approach, the observed value of the cosmological constant has to arise from the energy fluctuations of degrees of freedom located in the boundary of a spacetime region.     

Localization of Gravity in Brane World with Arbitrary Extra Dimensions

We study the induced 4-dimensional linearized Einstein field equations in an m-dimensional bulk space by means of a confining potential. We used the confining potential in this model to localized gravitons on the brane. It is shown that in this approach the mass of graviton is quantized. The cosmological constant problem is also addressed within the context of this approach. We show that the difference between the values of the cosmological constant in particle physics and cosmology stems from our measurements in two different scales, small and large.     

String inspired brane world cosmology

We consider brane world scenarios including the leading correction to the Einstein-Hilbert action suggested by superstring theory, the Gauss-Bonnet term. We obtain and study the complete set of equations governing the cosmological dynamics. We find they have the same form as those in Randall-Sundrum scenarios but with time-varying four-dimensional gravitational and cosmological constants. By studying the bulk geometry we show that this variation is produced by bulk curvature terms parametrized by the mass of a black hole. Finally, we show there is a coupling between these curvature terms and matter that can be relevant for early universe cosmology.     

Letter: Inflationary Dilatonic de Sitter Universe from Super Yang-Mills Theory Perturbed by Scalars and Spinors

In this paper a quantum N = 4 super Yang-Mills theory perturbed by dilaton-coupled scalars and spinor fields, is considered. The induced effective action for such a theory is calculated on a dilaton-gravitational background using the conformal anomaly found via the AdS/CFT correspondence. Considering such an effective action (using the large N method) as a quantum correction to the classical gravity action with cosmological constant, we study the effect from the dilaton on the scale factor (this corresponds to an inflationary universe without dilaton). It is shown that, depending on the initial conditions for the dilaton, the dilaton may slow down, or accelerate, the inflation process. At late times, the dilaton is decaying exponentially. Different possible cases corresponding to a dilatonic dS Universe are analyzed with respect to the equations of motion.     

Induced cosmology on a codimension-2 brane in a conical bulk

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.     

Cosmological compactification in Kaluza-Klein model and time-dependent cosmological term

Einstein's equations for the generalized (4+D)-dimensional Robertson-Walker model are solved taking the conformally invariant action for the matter field. Compactification of this model is discussed and the compactification time/compactification mass scale for different values ofD is calculated. The resulting 4-dimensional action for gravity is obtained. It is found that a time-dependent cosmological constant is induced which is very large when the cosmic time is small and very small when the cosmic time is large.     

Effective Action for Scalar Fields in Two-Dimensional Gravity

We consider a general two-dimensional gravity model minimally or nonminimally coupled to a scalar field. The canonical form of the model is elucidated, and a general solution of the equations of motion in the massless case is reviewed. In the presence of a scalar field all geometric fields (zweibein and Lorentz connection) are excluded from the model by solving exactly their Hamiltonian equations of motion. In this way the effective equations of motion and the corresponding effective action for a scalar field are obtained. It is written in a Minkowskian space-time and does not include any geometric variables. The effective action arises as a boundary term and is nontrivial both for open and closed universes. The reason is that unphysical degrees of freedom cannot be compactly supported because they must satisfy the constraint equation. As an example we consider spherically reduced gravity minimally coupled to a massless scalar field. The effective action is used to reproduce the Fisher and Roberts solutions.     

Self-tuning and de Sitter brane intersections in 6-dimensional brane models

We study the self-tuning of general brane junctions and brane networks on 6-dimensional space-time. For general brane junctions, there may exist one fine-tuning among the brane tensions. For the brane networks, similar to the 5-dimensional self-tuning brane models, the brane tensions can be set arbitrarily and there exists a singularity for the metric and bulk scalar. If we want to regularize the singularity, we will introduce fine-tuning among the brane tensions. In addition, because the 4-dimensional cosmological constant we observe may be positive and very small, we discuss the brane network with de Sitter brane intersections by introducing a bulk scalar. Received: 8 November 2001 / Published online: 20 November 2002 RID="a" ID="a" Present address: Division of High Energy Physics, Argonne National Laboratory, Argonne IL 60439, USA RID="b" ID="b" Present address: School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA. E-mail: tli@sns.ias.edu     

A note on the generalized Friedmann equations for a thick brane

Within our thick brane approach previously used to obtain the cosmological evolution equations on a thick brane embedded in a five-dimensional Schwarzschild Anti-de Sitter spacetime it is explicitly shown that the consistency of these equations with the energy conservation equation requires that, in general, the thickness of the brane evolves in time. This varying brane thickness entails the possibility that both Newton’s gravitational constant G and the effective cosmological constant Λ₄ are time dependent.     

Localising gravity in composite monopole brane worlds without bulk cosmological constant

We study a 7-dimensional brane world scenario with a Ricci-flat 3-brane residing in the core of a composite monopole defect, i.e., a defect composed of a 't Hooft–Polyakov and a global monopole. Admitting a direct interaction between the two bosonic sectors of the theory, we analyse the structure of the space–time in the limits of small, respectively large direct interaction coupling constant. For large direct interaction, the global monopole disappears from the system and leaves behind a negative cosmological constant in the bulk such that gravity-localising solutions are possible without a priori introduction of a bulk cosmological constant.     

General solutions for a cosmological Robertsonwalker metric in the Brans-Dicke theory

The general vacuum solutions of the Brans-Dicke theory in a cosmological Robertson-Walker-type metric are explicitly given. Several families of solutions have properties which essentially differ from the conventional Einstein theory. The geometry is not uniquely determined by the equations of motion, raising doubts about the “Machian” character of the Brans-Dicke theory. The role of the cosmological constant is emphasized, in agreement with modern ideas of fundamental particle interactions.     

A braneworld universe from colliding bubbles

Much work has been devoted to the phenomenology and cosmology of the so-called braneworld universe, where the (3+1)-dimensional universe familiar to us lies on a brane surrounded by a (4+1)-dimensional bulk spacetime that is essentially empty except for a negative cosmological constant and the various modes associated with gravity. For such a braneworld cosmology, the difficulty of justifying a set of preferred initial conditions inevitably arises. The various proposals for inflation restricted to the brane only partially explain the homogeneity and isotropy of the resulting braneworld universe because the three-dimensional homogeneity and isotropy of the bulk must be assumed a priori. In this Letter we propose a mechanism by which a brane surrounded by AdS space arises naturally in such a way that the homogeneity and isotropy of both the brane and the bulk are guaranteed. We postulate an initial false vacuum phase of (4+1)-dimensional de Sitter, or possibly Minkowski, space subsequently decaying to a true vacuum of anti-de Sitter space, assumed discretely degenerate. This decay takes place through bubble nucleation. When two bubbles of the true AdS vacuum eventually collide, because of the degeneracy of the true AdS vacuum, a brane (or domain wall) inevitably forms separating the two AdS phases. It is on this brane that we live. The SO(3,1) symmetry of the collision geometry ensures the three-dimensional spatial homogeneity and isotropy of the universe on the brane as well as of the bulk. In the semi-classical (→0) limit, this SO(3,1) symmetry is exact. We sketch how the leading quantum corrections translate into cosmological perturbations.     

Solution of dirac equation in a singularity-free Kaluza-Klein cosmological model

The singularity-free solution of (4 + D) -dimensional Einstein field equations for the Kaluza-Klein cosmological model is obtained. Then the Dirac equations are solved in this model.     

Restoring holographic dark energy in brane cosmology

We present a generalized version of holographic dark energy arguing that it must be considered in the maximally subspace of a cosmological model. In the context of brane cosmology it leads to a bulk holographic dark energy which transfers its holographic nature to the effective 4D dark energy. As an application we use a single-brane model and we show that in the low energy limit the behavior of the effective holographic dark energy coincides with that predicted by conventional 4D calculations. However, a finite bulk can lead to radically different results.     

Warped compactification to de Sitter space

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)$(4+n)$-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 localized on an inflating four-dimensional FLRW universe. This result helps establish that the ‘no-go’ theorem forbidding acceleration in ‘standard’ compactification of string/M-theory on physically compact spaces should not apply to a general class of warped supergravity models that allows at least one noncompact direction. We present solutions for which the size of the radial dimension takes a constant value in the large volume limit, providing an explicit example of spontaneous compactification.