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.     

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.     

Cylindrically symmetric cosmological models in Kaluza-Klein spacetime

We consider a non-diagonal cylindrically symmetric metric in the Kaluza-Klein spacetime. We obtain a number of homogeneous and inhomogeneous perfect fluid cosmological models, which include the 5-dimensional analogue of the recently found 4-dimensional non-singular stiff fluid model. Amongst the homogeneous models, which are all as expected big-bang singular, there is the 5-dimensional version of the Friedman-Robertson-Walker flat model.     

Cosmological application on five-dimensional teleparallel theory equivalent to general relativity

A theory of(4+1)-dimensional gravity has been developed on the basis of which equivalent to the theory of general relativity by teleparallel.The fundamental gravitational field variables are the 5-dimensional(5D) vector fields(pentad),defined globally on a manifold M,and gravity is attributed to the torsion.The Lagrangian density is quadratic in the torsion tensor.We then apply the field equations to two different homogenous and isotropic geometric structures which give the same line element,i.e.,FRW in five dimensions.The cosmological parameters are calculated and some cosmological problems are discussed.     

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：     

Gauge semi-simple extension of the Poincaré group

An approach to the cosmological term problem is proposed, using the gauge semi-simple tensor extension of the D-dimensional Poincaré group as a basis.     

Sketch of a New 5-dimensional Projective Unified Field Theory — Physical Predictions and Applications

Some years ago the author published a new version of a 5-dimensional Projective Unified Field Theory unifying gravitation, electromagnetism and scalarism. Geometrically this theory is mainly based on following 5-dimensional assumptions: symmetric metric tensor, Riemannian curvature, torsion, projector property of the basic quantities. A particular projection procedure leads from the 5-dimensional field equations and conservation laws to 4-dimensional ones. The 4-dimensional scheme of equations is interpreted physically. Special interest is taken in the energy projector, describing an electrically charged perfect fluid. Several physical predictions and applications are presented.     

The Electromagnetic Analogue of Some Gravitational Perturbations in Cosmology

Recently attention has been drawn to the fact that perfect fluid tensor perturbations (with perturbed vorticity and acceleration vanishing) of isotropic cosmological models have a perturbed Weyl tensor with electric part satisfying a linear, homogeneous, third-order wave equation while the magnetic part satisfies a linear, homogeneous, second-order wave equation. We construct an analogous class of electromagnetic test fields in the isotropic cosmological models for which the electric vector satisfies a third-order, linear and homogeneous wave equation while the magnetic vector satisfies a second-order, linear and homogeneous wave equation. If the perfect fluid has an equation of state we give a simplified derivation of the authors' previous perturbation analysis describing gravitational waves carrying arbitrary information. We also present the analogous solutions of Maxwell's equations which contain electromagnetic waves conveying arbitrary information.     

Rotating cosmological models of Bianchi type VIII

We find cosmological solutions with rotation of Bianchi type VIII for the energy-momentum tensor of a perfect fluid with heat flow.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 98–103, May, 1989.In conclusion the author expresses thanks to the participants in Professor D. D. Ivanenko's seminar for helpful discussions.     

Hydrodynamics in 5-Dimensional Cosmological Special Relativity

The dynamics of a perfect fluid is studied in 5-dimensional special relativity, a framework which can be considered the 5-d generalization of cosmological special relativity as well as the flat specialization of 5-d brane world theory. This picture, as described in an earlier paper, directly includes a particle production mechanism. Here it is showed that the source of particle production vanishes if the fluid is isentropic. Moreover it is showed that the hydrodynamical equations can be interpreted in terms of a scale factor, giving rise to a set of equations which simulate in a sense Friedmann cosmology.     

Models of G time variations in diverse dimensions

A review of different cosmological models in diverse dimensions leading to a relatively small time variation in the effective gravitational constant G is presented. Among them: the 4-dimensional (4-D) general scalar-tensor model, the multidimensional vacuum model with two curved Einstein spaces, the multidimensional model with the multicomponent anisotropic “perfect fluid”, the S-brane model with scalar fields and two form fields, etc. It is shown that there exist different possible ways of explaining relatively small time variations of the effective gravitational constant G compatible with present cosmological data (e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional cosmological models with different matter sources. The experimental bounds on ? may be satisfied either in some restricted interval or for all allowed values of the synchronous time variable.     

Black holes and membranes in higher-dimensional theories with dilaton fields

We consider scale invariant theories which couple gravity to Maxwell fields and antisymmetric tensor fields with a dilaton field. We exhibit in a unified way solutions representing black hole, space-time membrane, vortex and cosmological solutions. Their physical properties depend sensitively on the coupling constant of the dilaton field, there being critical value separating qualitatively different types of behaviour, e.g. the temperature of a charged black hole in the extreme limit. It is also shown that compactification into the 4-dimensional Minkowski space in terms of a membrane solution is possible in 10-dimensional supergravity model.     

The magnetic part of the Weyl tensor,and the expansion of discrete universes

We examine the effect that the magnetic part of the Weyl tensor has on the large-scale expansion of space. This is done within the context of a class of cosmological models that contain regularly arranged discrete masses, rather than a continuous perfect fluid. The natural set of geodesic curves that one should use to consider the cosmological expansion of these models requires the existence of a non-zero magnetic part of the Weyl tensor. We include this object in the evolution equations of these models by performing a Taylor series expansion about a hypersurface where it initially vanishes. At the same cosmological time, measured as a fraction of the age of the universe, we find that the influence of the magnetic part of the Weyl tensor increases as the number of masses in the universe is increased. We also find that the influence of the magnetic part of the Weyl tensor increases with time, relative to the leading-order electric part, so that its contribution to the scale of the universe can reach values of \(\sim \)1%, before the Taylor series approximation starts to break down.     

Magnetized anisotropic cosmological models with varying Λ

Some anisotropic homogeneous cosmological models with electromagnetic field are obtained in presence of a perfect fluid. The source of the magnetic field is due to an electric current produced along the x-axis. Without assuming any ad hoc law, we obtain a cosmological constant as a decreasing function of time which is supported by results from recent supernovae Ia observations. The behaviour of the electromagnetic field tensor together with some physical aspects of the model are also discussed.     

Analytical Solution of a Wave Equation in Cosmology

In this paper we derive a wave equation based on a cosmological model of the universe expansion in the four-dimensional space-velocity. An analytical solution of this equation is obtained using Nikiforov-Uvarov mathematical method. In this procedure we use the solutions of the Einstein gravitational field equations for the perfect fluid energy-momentum tensor.     

The Scalar Fields with Negative Kinetic Energy, Dark Matter and Dark Energy

The inhomogeneous cosmological model with generalized nonstatic Majumdar-Papapetrou metric is considered. The scalar field with negative kinetic energy and some usual matter sources of the gravitational field such as two-component nonlinear sigma model and perfect fluid are presented. Some exact solutions in these models are obtained and analyzed. In particular it is shown that the latent mass effect and effect of accelerating expansion (quintessence) of the Universe exist in these models. The 5-dimensional generalization of the model is presented, too.     

Higher Dimensional Spherically Symmetric Expanding Wormholes in Einstein’s Gravity

We present (n+1)-dimensional expanding structures in a cosmological background. Due to the expansion of spacetime the throat of wormholes enlarge with time. These solutions are examined in the Einstein’s framework. A general linear relation between diagonal elements of an anisotropic energy-momentum tensor is assumed and the spherically symmetric structures are obtained. Solutions include naked singularity and expanding wormholes in an open universe. The traversibility of wormhole solutions is explored and we find that they are basically traversable. Finally, we consider the corresponding energy-momentum tensor properties and specially take into account the standard energy conditions.     

Models of G time variations in diverse dimensions

A review of different cosmological models in diverse dimensions leading to a relatively small time variation in the effective gravitational constant G is presented. Among them: the 4-dimensional (4-D) general scalar-tensor model, the multidimensional vacuum model with two curved Einstein spaces, the multidimensional model with the multicomponent anisotropic “perfect fluid”, the S-brane model with scalar fields and two form fields, etc. It is shown that there exist different possible ways of explaining relatively small time variations of the effective gravitational constant G compatible with present cosmological data (e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional cosmological models with different matter sources. The experimental bounds on Ġ may be satisfied either in some restricted interval or for all allowed values of the synchronous time variable.      

A Plane-Symmetric Inhomogeneous Cosmological Model of Perfect Fluid Distribution with Electromagnetic Field I

A plane-symmetric inhomogeneous cosmological model of perfect fluiddistribution with electro-magnetic field is obtained. F₁₂ is the non-vanishing component of electromagnetic field tensor. To get a deterministic solution, we assume the free gravitational field is Petrov type-II non-degenerate. Some physical and geometric properties of the model are also discussed.     

Alternative Inflationary Scenario Due to Compact Extra Dimensions

The main goal of this paper is to give an alternative interpretation of space-like and time-like extra dimensions as a primary factor for inflation in the early universe. We introduce the 5-dimensional perfect fluid and compare the energy-momentum tensor for the bulk scalar field with space-like and time-like extra dimensions. It is shown, that additional dimensions can imply to negative pressure in the slow roll regime in the early higher-dimensional world.