Matching Spherical Dust Solutions to Construct Cosmological Models

Conditions for smooth cosmological models are set out and applied to inhomogeneous spherically symmetric models constructed by matching together different Lemaître–Tolman–Bondi solutions to the Einstein field equations. As an illustration the methods are applied to a collapsing dust sphere in a curved background. This describes a region which expands and then collapses to form a black hole in an Einstein de Sitter background. We show that in all such models if there is no vacuum region then the singularity must go on accreting matter for an infinite LTB time.     

Local thermal equilibrium and ideal gas Stephani universes

The Stephani universes that can be interpreted as an ideal gas evolving in local thermal equilibrium are determined. Five classes of thermodynamic schemes are admissible, which give rise to five classes of regular models and three classes of singular models. No Stephani universes exist representing an exact solution to a classical ideal gas (one for which the internal energy is proportional to the temperature). But some Stephani universes may approximate a classical ideal gas at first order in the temperature: all of them are obtained. Finally, some features about the physical behavior of the models are pointed out.This revised version was published online in April 2005. The publishing date was inserted.     

Integrable multicomponent perfect fluid multidimensional cosmology. I

Multidimensional cosmological models with a space-time consisting ofn (n 2) Einstein spaces are investigated for a special class of multicomponent perfect fluid as a matter source. The dynamical behaviour of the universe is described. In the case of static internal spaces the external space evolves like a Friedmann universe with changing effective equation of state. Some of the models considered are integrable and classical as well as quantum solutions are found. Some of them represent wormholes. Quantum wormholes have a discrete spectrum.     

Letter: Self-Similar Bianchi Type VIII and IX Models

It is shown that in transitively self-similar spatially homogeneous tilted perfect fluid models the symmetry vector is not normal to the surfaces of spatial homogeneity. A direct consequence of this result is that there are no self-similar Bianchi VIII and IX tilted perfect fluid models. Furthermore the most general Bianchi VIII and IX spacetime which admits a four dimensional group of homotheties is given.     

On the stochasticity in relativistic cosmology

It was shown earlier by I. M. Lifshitz and two of us that the evolution of the relativistic cosmological models towards the singularity undergoes spontaneous stochastization.⁽¹⁾ In the present paper it is shown that the statistical parameters of this evolution can be calculated in an exact manner. From the point of view of the general ergodic theory we deal here with a specific mode of stochastization of a deterministic dynamical system with a five-dimensional phase space. The knowledge of the source of stochasticity makes it possible to develop a quantitative statistical theory with appreciable completeness.     

Tachyonic Dark Matter

Recent attempts to explain the dark matter and energy content of the universe have involved some radical extensions of standard physics, including quintessence, phantom energy, additional space dimensions, and variations in the speed of light. In this paper I consider the possibility that some dark matter might be in the form of tachyons. I show that, subject to some reasonable assumptions, a tachyonic cosmological fluid would produce distinctive effects, such as a surge in quantum vacuum energy and particle creation, and a change in the conventional temperature–time relation for the normal cosmological material. Possible observational consequences are discussed.     

Cosmological Constant and Stability of the Cosmological Models

The importance of cosmological constant for the cosmological models is given. The variations of the cosmological model for parameters λ and k were discussed respectively. Near λ = 0, the cosmological model is unstable with the change of λ, and near λ = β = 0, the cosmological model is unstable with the change of k. So when we consider the stable cosmological model, we must consider the nonzero cosmological constant.     

Letter: A Study of Asymptotic Behavior of Homogeneous Cosmological Models with a Varying Cosmological Constant in Einstein-Cartan Theory: Cosmic No-Hair Theorem

We have investigated cosmic no-hair theorem with varying cosmological constant in homogeneous anisotropic Bianchi-models for Einstein-Cartan theory. We have taken the variation of to be as the square of the extrinsic curvature scalar and asymptotic behavior has been studied.     

Nonsingular cosmological models: the massive scalar field case

The nonminimal coupling of a massive self-interacting scalar field with a gravitational field is studied. Spontaneous symmetry breaking occurs in the open universe even when the sign on the mass term is positive. In contrast to grand unified theories, symmetry breakdown is more important for the early universe and it is restored only in the limit of an infinite expansion. Symmetry breakdown is shown to occur in flat and closed universes when the mass term carries a wrong sign. The model has a naturally defined effective gravitational coupling coefficient which is rendered time-dependent due to the novel symmetry breakdown. It changes sign below a critical value of the cosmic scale factor indicating the onset of a repulsive field. The presence of the mass term severely alters the behaviour of ordinary matter and radiation in the early universe. The total energy density becomes negative in a certain domain. These features make possible a nonsingular cosmological model for an open universe. The model is also free from the horizon and the flatness problems.     

Plane Symmetric Viscous Fluid Cosmological Models with Varying <Emphasis Type="Italic">Λ</Emphasis>-Term

Plane symmetric viscous fluid cosmological models of the universe with a variable cosmological term are investigated. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density whereas the coefficient of shear viscosity is to be proportional to rate of expansion in the model. We have also obtained a special model in which the shear viscosity is assumed to be zero. The cosmological constant Λ is found to be a decreasing function of time and a positive which is supported by results from recent supernovae Ia observations. Some physical and geometric properties of the models are also discussed.     

一类无奇点宇宙模型

按照Penrose-Hawking的奇点定理,在场源物质无旋、无加速且能量密度满足条件ρ+3p≥0的宇宙模型中一定存在奇点.本文研究了场源物质有旋时的无奇点宇宙模型,获得了几种无奇点的宇宙解.     

A charged spherically symmetric solution

We find a solution of the Einstein-Maxwell system of field equations for a class of accelerating, expanding and shearing spherically symmetric metrics. This solution depends on a particularansatz for the line element. The radial behaviour of the solution is fully specified while the temporal behaviour is given in terms of a quadrature. By setting the charge contribution to zero we regain an (uncharged) perfect fluid solution found previously with the equation of statep = μ + constant, which is a generalisation of a stiff equation of state. Our class of charged shearing solutions is characterised geometrically by a conformal Killing vector.     

Study of the Magnitude-Redshift Relation for Type Ia Supernovae in a Model Resulting from a Ricci-Symmetry

Models with a dynamic cosmological term (t) are becoming popular as they solve the cosmological constant problem in a natural way. Instead of considering any ad-hoc assumption for the variation of , we consider a particular symmetry, the contracted Ricci-collineation along the fluid flow, in Einstein's theory. We show that apart from having interesting properties, this symmetry does demand to be a function of the scale factor of the Robertson-Walker metric. In order to test the consistency of the resulting model with observations, we study the magnitude-redshift relation for the type Ia supernovae data from Perlmutter et al. The data fit the model very well and require a positive non-zero and a negative deceleration parameter. The best-fitting flat model is obtained as ₀ 0.5 with q ₀ –0.2.     

Density-metric unimodular gravity: Vacuum maximal symmetry

We have investigated the vacuum maximally symmetric solutions of recently proposed density-metric unimodular gravity theory. The results are widely different from inflationary scenario. The exponential dependence on time in deSitter space is substituted by a power law. Open space–times with non-zero cosmological constant are excluded.     

Clumps into Voids

We consider a spherically symmetric distribution of dust and show that it is possible, under general physically reasonable conditions, for an overdensity to evolve to an underdensity (and vice versa). We find the conditions under which this occurs and illustrate it on a class of regular Lemaître–Tolman–Bondi (LTB) solutions. The existence of this phenomenon, if verified, would have the result that the topology of density contours, assumed fixed in standard structure formation theories, would have to change and that luminous matter would not trace the dark matter distribution so well.     

PARAMETRIC SOLUTION OF CERTAIN NONLINEAR DIFFERENTIAL EQUATIONS IN COSMOLOGY

We obtain in terms of the Weierstrass elliptic ?-function, sigma function, and zeta function an explicit parametrized solution of a particular nonlinear, ordinary differential equation. This equation includes, in special cases, equations that occur in the study of both homogeneous and inhomogeneous cosmological models, and also in the dynamic Bose–Einstein condensates–cosmology correspondence, for example.     

Anisotropic cosmological models and generalized scalar tensor theory

In this paper generalized scalar tensor theory has been considered in the background of anisotropic cosmological models, namely, axially symmetric Bianchi-I, Bianchi-III and Kortowski-Sachs space-time. For bulk viscous fluid, both exponential and power-law solutions have been studied and some assumptions among the physical parameters and solutions have been discussed.     

Bianchi Type I Universe Models with Irreversible Matter Creation

The effects of matter creation on the evolution and dynamics of an anisotropic Bianchi type I space–time is investigated in the framework of open thermodynamic systems theory. For a cosmological fluid obeying a Zel'dovich type equation of state =p and with particle creation rate proportional to the square of the mean Hubble function and to the energy density of matter, respectively, the general solution of the gravitational field equations can be expressed in an exact parametric form. Generically all models start from a non-singular state. In the large time limit anisotropic cosmological models with particle creation rate proportional to the square of the Hubble function end in an isotropic flat (inflationary or non–inflationary) phase while models with particle source function proportional to the energy density of matter do not isotropize, ending in a Kasner–type geometry.