Cosmological Dynamics of Brane Models and Vacuum Effects

The imposition of boundary conditions on the background fields of brane-world models leads to nonzero vacuum averages for the corresponding energy-momentum tensor. Methods from the qualitative theory of dynamic systems are used in this paper to study the cosmological evolution generated by this tensor. All the possible types of cosmological dynamics are examined for models with homogeneous and isotropic subspaces on the branes and the behavior of the corresponding solutions is studied in the early and late stages of evolution.     

Cosmological solutions of the Einstein-Yang equation and of the Einstein equation

For the Robertson-Walker metric for a homogeneous and isotropic universe, I have derived explicit solutions of the Einstein-Yang equation (interior torsion-free solutions for a spin-less ideal fluid) and hence found certain solutions of the Einstein field equation for the radiation-dominated phase of the early universe.     

Classical Matter Fields in Homogeneous Cosmological Models

The behaviour of classical massive scalar and vector fields as sources of homogeneous world models is examined. The consequence of the violation of the strong energy condition by the massive scalar field for the evolution of an cosmological model is discussed.     

Cosmological Models with Variable G and Λ

Einstein's equations with variable gravitational and cosmological constants are considered in the presence of a perfect fluid for the anizotropic Bianchi I universe in a way which conserving the energy-momentum tensor. Two solutions are found, one of which the cosmological term varies inversely with power law of time. The other of which cosmological term is constant.     

Two-Fluid Bianchi Type II Cosmological Models

In this paper we present a class of solutions of Einstein's field equations describing two-fluid models of the universe in a locally rotationally symmetric Bianchi type II space-time. In these models one fluid is the radiation distribution which represents the cosmic microwave background and the other fluid is the perfect fluid representing the matter content of the universe. It is found that both the fluids are comoving in the locally rotationally symmetric Bianchi type II space-time. The behaviour of the radiation density, matter density, the ratio of the matter density to the radiation density and the pressure has been discussed. A subclass of solutions is found to describe models of a spatially homogeneous and partially isotropic universe evolving from a radiation dominated era to a pressure free matter dominated era. This revised version was published online in July 2006 with corrections to the Cover Date.     

Some Cosmological Models in Scalar-Tensor Theory of Gravitation

Field equations in a scalar-tensor theory of gravitation proposed by Saezand Ballester (1985) are obtained with the aid of (i) Friedmann-type metric (ii) a non static plane symmetric metric and (iii) spatially homogeneous Bianchi type – III metric. Some cosmological models corresponding to perfect fluid and bulk viscous fluid are presented. Physical and kinematical properties of the models are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Cylindrically-Symmetric and Inhomogeneous Cosmological Models with Viscous Fluid

In this paper, the Einstein field equations have been solved for cylindrically symmetric and inhomogeneous cosmological models with viscous fluid. Various physical and geometrical properties of the models are also discussed.     

Some Viscous Fluid Cosmological Models in General Relativity

The motivation of this paper is to investigate two viscous fluid cosmological models in General Relativity in which the expansion is only in two directions i.e. one of the Hubble parameters is zero. In the first model, coefficient of shear viscosity is assumed to be constant while in the second model, the coefficient of shear viscosity is proportional to the rate of expansion in the model. Here no additional condition is assumed except for coefficient of shear viscosity. These models are new and different from those models obtained by Bali and Jain (1987, 1988) in which free gravitational field was assumed to be Petrov Type D and non-degenerate for Marder (1958) metric and coefficient of shear viscosity is proportional to the rate of expansion in the model. The various physical and geometrical aspects of the models are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Higher Dimensional FRW Cosmological Models in Self-Creation Theory

The field equations of Barber's (1982) second self-creation theory of gravitation are solved for 5D Friedmann-Robertson-Walker space time using perfect fluid energy momentum tensor. By assuming an equation of state p= ε ρ, (0 ≤ ε ≤ 1), the solutions of the field equations, in different scenarios, in Barber's second self-creation theory are presented and discussed. Some properties of these models are also discussed.     

Anisotropic Bianchi Type-II Cosmological Models in Self-Creation Cosmology

Totally anisotropic Bianchi type-II cosmological solutions are presented in Barber's second self-creation theory of gravitation both in vacuum and in the presence of stiff-matter. The corresponding cosmological models have no finite singularity. The stiff-matter model gives essentially an empty universe for large time. Some physical and kinematical properties of the models are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Inhomogeneous Cylindrically-Symmetric Models with Varying Cosmological Term

We consider Einstein's equations with variable cosmological constant in the presence of a perfect fluid for the inhomogeneous cylindrically-symmetric space–time. We find two solutions under this conditions and analyze our solutions with respect to the constants.     

Λ Varying Cosmological Models with Viscous Fluid

Evolution of a homogeneous, isotropic Universe with flat geometry filled with a viscous fluid is investigated in presence of a variable cosmological Λ. A non-singular solution leading to a variable deceleration parameter is obtained which reduces to the solution of Murphy in the ‘no Λ limit’ and to the recent solution of Vishwakarma in the context of ‘a Machian model of dark energy’ in the ‘no viscosity’ limit.     

Some Bianchi Type I Viscous Fluid Cosmological Models with a Variable Cosmological Constant

Some Bianchi type I viscous fluid cosmological models with a variable cosmological constant are investigated in which the expansion is considered only in two direction i.e. one of the Hubble parameter is zero. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density whereas the coefficient of shear viscosity is considered as constant in first case whereas in other case it is taken as proportional to scale of expansion in the model. The cosmological constant Λ is found to be positive and is a decreasing function of time which is supported by results from recent supernovae Ia observations. Some physical and geometric properties of the models are also discussed.     

Early Cosmological Models with Bulk Viscosity in Brans-Dicke Theory

The effect of time dependent bulk viscosity on the evolution of Friedmann models with zero curvature in Brans-Dicke theory is studied. The solutions of the field equations with ‘gamma-law’ equation of state p = (γ-1) ρ, where γ varies continuously as the Universe expands, are obtained by using the power-law relation φ = bR ⁿ , which lead to models with constant deceleration parameter. We obtain solutions for the inflationary period and radiation dominated era of the universe. The physical properties of cosmological solutions are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Quintessential Cosmology Novel Models of Cosmological Structure Formation

We examine the possibility that a substantial fraction of the total energy density in a spatially flat Universe is composed of a time-dependent and spatially inhomogeneous component whose equation-of-state differs from that of baryons, neutrinos, dark matter, or radiation. In this lecture, we report on our investigations of the case in which the additional energy component, dubbed "quintessence", is due to a dynamical scalar field evolving in a potential. We have computed the effects on the background cosmological evolution, the cosmic microwave background (CMB) and mass power spectrum, finding a broad range of cosmologically viable models. We stress three important features of the quintessence or Q-component: the time evolution of the equation-of-state; the length-scale dependence of the speed of propagation of the fluctuations in the Q-component; and, the contribution of quintessence fluctuations to the CMB anisotropy spectrum. This revised version was published online in July 2006 with corrections to the Cover Date.     

Viscous Fluid Cosmological Models in a Bianchi Type I Universe

Exact solutions of the gravitational field equations for a Bianchi type I anisotropic space-time, filled with a viscous cosmological fluid obeying an equation of state of the form p = , 0 1, are obtained. We investigate both the viscous Zeldovich ( = 1) and < 1 fluid cases, with constant and time varying (proportional to the mean Hubble factor) shear and bulk viscosity coefficients. It is shown that independently of the matter content, the equation of state and the time dependence of the shear and bulk viscosity coefficients, a viscous Bianchi type I universe experiences a transition to an inflationary era. Due to dissipative processes, the mean anisotropy and the shear of the Bianchi type I universe tend very rapidly to zero.