Using Energy Conditions to Distinguish Brane Models and Study Brane Matter

Current universe （assumed here to be normal matter on the brahe） is pressureless from observations. In this case the energy condition is po ≥ 0 and po =O. By using this condition, brahe models can be distinguished. Then, assuming arbitrary component of matter in DGP model, we use four known energy conditions to study the matter on the brahe. If there is nonnormal matter or energy （for example dark energy with w 〈-1/3） on the brane, the universe is accelerated.     

Using Energy Conditions to Distinguish Brane Models and Study Brane Matter

Current universe (assumed here to be normal matter on the brane) is pressureless from observations. In this case the energy condition is ρ₀≥0 and p₀=0. By using this condition, brane models can be distinguished. Then, assuming arbitrary component of matter in DGP model, we use four known energy conditions to study the matter on the brane. If there is nonnormal matter or energy (for example dark energy with w<-1/3) on the brane, the universe is accelerated.     

Abundance of Asymmetric Dark Matter in Brane World Cosmology

Relic abundance of asymmetric Dark Matter particles in brane world cosmological scenario is investigated in this article. Hubble expansion rate is enhanced in brane world cosmology and it affects the relic abundance of asymmetric Dark Matter particles. We analyze how the relic abundance of asymmetric Dark Matter is changed in this model. We show that in such kind of nonstandard cosmological scenario, indirect detection of asymmetric Dark Matter is possible if the cross section is small enough which let the anti-particle abundance kept in the same amount with the particle. We show the indirect detection signal constraints can be used to such model only when the cross section and the 5-dimensional Planck mass scale are in appropriate values.     

Crossing w=1 in Gauss-Bonnet Brane World with Induced Gravity

Recent type Ia supernovas data seemingly favor a dark energy model whose equation of state w（z） crosses -1 very recently, which is a much more amazing problem than the acceleration of the universe. In this paper we show that it is possible to realize such a crossing without introducing any phantom component in a Gauss-Bonnet brane worm with induced gravity, where a four-dimensional curvature scalar on the brahe and a five-dimensional Gauss-Bonnet term in the bu/k are present. In this realization, the Gauss-Bonnet term and the mass parameter in the bulk play a crucial role.     

Letter: String Cosmology in Brane World Scenarios

We present exact solutions of the gravitational field equations in the generalized Randall-Sundrum model for an anisotropic brane with Bianchi I & V geometry and string dust as the matter source. We assume the Weyl tensor in the bulk has vanishing projection on the brane and examine the different equations of state, for the string dust system. Exact analytic solutions are possible only in few cases.     

Crossing w = -1 in Gauss-Bonnet Brane World with Induced Gravity

Recent type Ia supernovas data seemingly favor a dark energy model whose equation of state w(z) crosses -1 very recently, which is a much more amazing problem than the acceleration of the universe. In this paper we show that it is possible to realize such a crossing without introducing any phantom component in a Gauss-Bonnet brane world with induced gravity, where a four-dimensional curvature scalar on the brane and a five-dimensional Gauss-Bonnet term in the bulk are present. In this realization, the Gauss-Bonnet term and the mass parameter in the bulk play a crucial role.     

Symplectic Structure in Brane Mechanics

This paper treats the generalization to brane dynamics of the covariant canonical variational procedure leading to the construction of a conserved bilinear symplectic current in the manner originally developed by Witten, Zuckerman, and others in the context of field theory. After a general presentation, including a review of the relationships between the various (Lagrangian, Eulerian, and other) relevant kinds of variation, the procedure is illustrated by application to the particularly simple case of branes of the Dirac—Goto—Nambu type, in which internal fields are absent.     

Coleman–de Luccia Instanton of the Second Order in a Brane World

The second order Coleman–de Luccia instanton and its action in the Randall–Sundrum type II model are investigated and the comparison with the results in Einstein’s general relativity is done in the present paper. PACS Numbers: 98.80.Cq.     

Null Geodesics in Five-Dimensional Manifolds

We analyze a class of 5D non-compact warped-product spaces characterized by metrics that depend on the extra coordinate via a conformal factor. Our model is closely related to the so-called canonical coordinate gauge of Mashhoon et al. We confirm that if the 5D manifold in our model is Ricci-flat, then there is an induced cosmological constant in the 4D sub-manifold. We derive the general form of the 5D Killing vectors and relate them to the 4D Killing vectors of the embedded spacetime. We then study the 5D null geodesic paths and show that the 4D part of the motion can be timelike—that is, massless particles in 5D can be massive in 4D. We find that if the null trajectories are affinely parameterized in 5D, then the particle is subject to an anomalous acceleration or fifth force. However, this force may be removed by reparameterization, which brings the correct definition of the proper time into question. Physical properties of the geodesics—such as rest mass variations induced by a variable cosmological "constant," constants of the motion and 5D time-dilation effects—are discussed and are shown to be open to experimental or observational investigation.     

The Complete Brane Solution in D-Dimensional Coupled Gravity System

We present the complete explicit brane solution in D-dimensional coupled gravity system.     

A Study of Brane Solutions in D-Dimensional Coupled Gravity System

We use only the equation.of motion for an interacting system of gravity, dilaton and antisymmetric tensor to study the soliton solutions by making use of a Poincaré-invariant ansatz. We show that the system of equations is completely integrable and the solution is unique with appropriate boundary conditions. Some new classes of solutions are also given explicitly.     

A Cosmological Model of Holographic Brane Gravity

A cosmological scenario with two branes (A and B) moving in a 5-dimensional bulk is considered. As in the case of ecpyrotic and born-again braneworld models it is possible that the branes collide. The energy-momentum tensor is taken to describe a perfect barotropic fluid on the A-brane and a phenomenological time-dependent cosmological constant on the B-brane. The A-brane is identified with our Universe and its cosmological evolution in the approximation of a homogeneous and isotropic brane is analysed. The dynamics of the radion (a scalar field on the brane) contains information about the proper distance between the branes. It is demonstrated that the deSitter type solutions are obtained for late time evolution of the braneworld and accelerative behaviour is anticipated at the present time.     

Brane Formation and Cosmological Constraint on the Number of Extra Dimensions

Special relativity is generalized to extra dimensions and quantized energy levels of particles are obtained. By calculating the probability of particles' motion in extra dimensions at high temperature of the early universe, it is proposed that the branes may have not existed since the very beginning of the universe, but formed later. Meanwhile, before the formation, particles of the universe may have filled in the whole bulk, not just on the branes. This scenario differs from that in the standard big bang cosmology in which all particles are assumed to be in the 4D spacetime. So, in brane models, whether our universe began from a 4D big bang singularity is questionable. A cosmological constraint on the number of extra dimensions is also given which favors N ≥ 7.     

Asymmetric Brane-World Scenarios and Simulated Gravity

I review the main aspects of the simulated gravity that arises in brane-world models in which the reflection symmetry is broken. I recall its main aspects, show how a Newton-like force can be simulated on small scales, and discuss the post-Newtonian constraints as well as the cosmology of this model.     

On Spherically Symmetric Minimally Coupled Brane Worlds

For a static, spherically symmetric brane in the framework of the RS2 concept, we study the conditions under which the 4D tensor E _v, arising from the 5D Weyl tensor, vanishes on the brane. Gravity on the brane is then decoupled from the bulk geometry, it is the so-called minimally coupled brane world (MCBW). Assuming E _v =0 in the whole bulk, we try to solve the 5D Einstein equations G _AB + _5gAB =0 and obtain an overdetermined set of equations for functions of the radial coordinate. Some special solutions are found, among which are the well-known black string solution with the Schwarzschild metric on the brane and its generalizations with Schwarzschild–(A)dS on-brane metrics. It is concluded that a MCBW can be embedded, in general, in a bulk where E_v is not identically zero but only vanishes on the brane. We also present some previous results on the general properties of scalar fields on the brane and give an example of a wormhole supported by a scalar field in a MCBW.     

与额外维相关的膜宇宙模型

对引力场的能量\|动量和角动量守恒定律研究进展进行了总结。依此探讨了一般五维时空膜宇宙模型中的能量\|动量张量、 角动量张量以及它们的守恒定律。通过计算一个膜宇宙模型中的能动张量, 论证了该模型中“可见膜”上的引力非常弱, 这可认为是从引力的角度反映了规范层次问题。结果与一般的结论, 即引力系统总能量为零是一致的。同时, 分析了这个膜宇宙模型中的角动量张量, 计算了该模型中的总角动量, 讨论了暴涨Randall\|Sundren(RS)模型中的总角动量的一些性质。说明了在这类模型中总角动量的类空分量均为零, 这与普通RS模型是一样的。同时, 分析了RS模型中背景以及膜上的宇宙学常数, 发现在RS模型中五维背景宇宙学常数和两个膜上的真空能都能取它们的自然值。最后通过修改RS模型, 得到了一种可以产生很小的有效宇宙学常数的机制。We summarized both the general covariant energy\|momentum and angular momentum conservation law in the gravitational system and analyzed the general covariant energy\|momentum tensor of the gravitational system in general five\|dimensional cosmological in brane\|universe models. After calculating this energy\|momentum for the cosmological generalization of the Randall\|Sundrum(RS) model which includes the original RS model as the static limit, we are able to show that the weakness of the gravitation on the “visible” brane is a general feature of this model. This is the origin of the gauge hierarchy from a gravitational point of view. Our results are also consistent with the fact that a gravitational system has vanishing total energy. We also discussed the properties of the general covariant angular momentum in five\|dimensional brane-universe model. With calculation of the total angular momentum of this model, we analyzed the properties of the total angular momentum in the inflationary RS model. We pointed that the space-like components of the total angular momentum are zero while the others are non-zero, which agrees with the results from ordinary RS model. We also investigated the bulk cosmological constant and brane vacuum energies in RS model. We show that the five\|dimensional bulk cosmological constant and the vacuum energies of the two branes could take their natural values. Finally we argued how we can generate a small four-dimensional effective cosmological constant on the branes by modifying the original RS model.     

Stabilization of the Hierarchy in Brane-World Scenarios

We consider a class of warped brane models with topology M ₄ × × S¹/Z ₂, where is a D₂-dimensional compact manifold, and two branes are placed at the orbifold fixed points. In a scenario where supersymmetry is broken not far below the cutoff scale, the hierarchy between the electroweak and the Planck scales is generated by a combination of the redshift and the large volume effects. We evaluate the effective potential induced by bulk scalar fields in these models and show that it can stabilize the moduli and the hierarchy without fine-tuning, provided that the internal space is flat. We also comment on the relation between these models and the five-dimensional scalar-tensor models that describe them classically when the compactification scale is small.     

Brane Cosmology, Varying Speed of Light and Inflation in Models with One or More Extra Dimensions

We summarize the approach to brane cosmology known as mirage cosmology and use it to determine the Friedmann equation on a 3-brane embedded in different bulk spacetimes all with one or more extra dimensions. Usually, when there is more than one extra dimension the junction conditions, central to the usual brane world scenarios, are difficult to apply. This problem does not arise in mirage cosmology because the brane is treated as a test particle in the background spacetime. We discuss in detail the dynamics of a brane embedded in two specific 10D bulk spacetimes, namely Sch-AdS₅ × S₅ and a rotating black hole, and from the dynamics—which are now rather more complicated since the brane can move in all the extra dimensions—determine the new dark fluid terms in the brane Friedmann equation. Some of these, such as the cosmological constant term, are seen to be bulk dependent. We then show explicitly how this mirage cosmology approach matches with the familiar junction condition approach when there is just one extra dimension. The issue of a varying speed of light in mirage cosmology is addressed and we find a scenario in which c _eff always increases, tending asymptotically to c ₀ as the universe expands. Finally some comments are made regarding brane inflation and limitations of the mirage cosmology approach are also discussed.     

Phantom Divide Crossing on Brane World

We study the RSII brane world corrected by the four-dimensional scalar curvature and five-dimensional Gauss-Bonnet curvature. The energy transfer between brane and bulk is also taken into account. Parameterizing the energy transfer, the resulting Friedmann equation on brane is solved at low energy. It is shown that phantom divide crossing may be achieved in the braneworld model with wide possibilities, embodying the combined effect of brane-bulk energy transfer, curvature corrections, and the fine-turning mechanics.     

新型椭球形窗口零位检测技术研究

椭球形窗口的检测技术严重阻碍其成功应用。首先简要介绍了目前普遍使用的非球面检测技术,并针对椭球形窗口大倾斜、大偏心、深非球面的特点,基于零位补偿检测法原理,设计了一种适合椭球形窗口检测的改进型Offner零位补偿检测系统。检测系统包括补偿镜、场镜和标准球面参考镜,检测系统工作原理为:干涉仪出射平行光线通过补偿镜及场镜产生修正波前,通过椭球形窗口照射到标准球面反射镜,并按原光路返回与参考光线干涉,其干涉结果显示出椭球形窗口的面形偏差。实现了对椭球形窗口的高精度全口径一次检测并给出了完整的设计结果。检测了长径比为1.0,口径为110mm的椭球形窗口,其波前残余波像差均方根值为0.0052λ。设计结果为实际使用提供了一定的参考。