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.     

Some Homogeneous Bianchi type IX Viscous Fluid Cosmological Models with a Varying Λ

Some Bianchi type IX viscous fluid cosmological models are investigated. To get a solution, a supplementary condition between metric potentials is used. 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 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 observations. Some physical and geometric properties of the models are also discussed.     

Early Viscous Fluid Cosmological Model with Zero-Rest-Mass Scalar Fields

Einstein field equations are considered for zero-curvature Robertson-Walker models in the case of a viscous fluid distribution interacting with zero-rest-mass scalar fields. Exact solutions are obtained for two different phases of the early universe viz. the inflationary phase and the radiation-dominated phase, by using the 'gamma-law' equation of state p = (-1). The index describing the material content varies continuously with cosmological time. The gravitational 'constant' and bulk viscosity are both allowed to depend on the cosmic time. Some physical properties of the cosmological models are also discussed.     

Bianchi Type-V Bulk Viscous Fluid String Dust Cosmological Model In General Relativity

Bianchi Type-V bulk viscous fluid string dust cosmological model in General Relativity is investigated. It has been shown that if coefficient of bulk viscosity (ζ) is inversely proportional to the expansion (θ) in the model then string cosmological model for Bianchi Type-V space-time is possible. In absence of bulk viscosity (ζ), i.e. when ζ → 0, then there is no string cosmological model for Bianchi Type-V space-time. The physical and geometrical aspects of the model are also discussed.     

Expanding and shearing inhomogeneous cosmological models for viscous fluid distributions with electromagnetic field

Some inhomogeneous viscous fluid cosmological models in the presence of an electromagnetic field for cylindrical symmetry are obtained. To get a determinate solution, it is assumed that the coefficient of shear viscosity is proportional to the rate of expansion. The paper also discusses the behaviour of the model when viscosity is absent and comments on some other physical properties.     

Cosmological mass model in general relativity

Relativistic cosmological field equations are obtained for a non-static stationary Bertotti-Robinson-type space-time for interacting perfect fluid and electromagnetic field. The cosmological solution to the field equations are obtained and the nature of the electromagnetic field as well the perfect fluid are studied. The electromagnetic field generated here corresponds to a special generic case and the perfect fluid distribution degenerates into a barotropic perfect fluid with equation of statep+=0, >0. It is shown here that the interacting barotropic fluid can generate gravitation only when the cosmological constant being a function ofx in a dynamic field.     

Tilted bianchi type v bulk viscous cosmological models in general relativity

Conformally flat tilted Bianchi type V cosmological models in presence of a bulk viscous fluid and heat flow are investigated. The coefficient of bulk viscosity is assumed to be a power function of mass density. Some physical andgeometric aspects of the models are also discussed.     

Cosmological solution in wesson's 5D theory of gravity

Cosmological solutions that obey the perfect fluid equation of state in Wesson's gravitational theory are presented assuming that the fifth dimension subspace is also homogeneous and isotropic like the usual homogeneous isotropic cosmological model. It is shown that the scale factor scales as for the vanishing fifth component of the energy momentum tensor. The role of the fifth component as a cosmological constant is remarked, and an inflationary model is thus obtained.     

Isotropic Homogeneous Universe with a Bulk Viscous Fluid in Lyra Geometry

Exact solutions are obtained for an isotropic homogeneous universe with a bulk viscous fluid in the cosmological theory based on Lyra’s geometry. The viscosity coefficient of the bulk viscous fluid is assumed to be a power function of the mass density. Cosmological models with time dependent displacement field have been discussed for a constant value of the deceleration parameter. Finally some possibilities of further problems and their investigations have been pointed out.     

Some expanding and shearing viscous fluid cosmological models in general relativity

Two cylindrically-symmetric cosmological models representing viscous fluid distributions when free-gravitational field of typeD where coefficient of shear viscosity is assumed to be proportional to the rate of expansion, are obtained. The behaviour of the models in the absence of viscosity and other physical properties are also discussed.     

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.     

Tilted Bianchi type I cosmological models filled with disordered radiation in general relativity revisitedD

Tilted Bianchi type I cosmological models filled with disordered radiation in presence of a bulk viscous fluid and heat flow are investigated. The coefficient of bulk viscosity is assumed to be a power function of mass density. Some physical and geometric properties of the models are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bianchi Type I String Cosmological Models with Bulk Viscosity and Magnetic Field

Some locally rotationally symmetric (LRS) Bianchi type I cosmological models for a cloud string with bulk viscosity and magnetic field are presented. Where an equation of state ρ = kλ and a relation between metric potential R = AS ⁿ are considered. The solution describes a shearing and nonrotating model with a big bang start. In the absence of magnetic field it reduces to a string model with bulk viscosity, where the relation between the coefficient of bulk viscosity and energy density is ζ ∝ ρ^1/2. After choosing k = , it further reduces to a string model without viscosity and magnetic field. This revised version was published online in July 2006 with corrections to the Cover Date.     

Viscous inflationary universe models

The research on viscous cosmological models is reviewed and carried further. Inflationary cosmological models of Bianchi type-I with shear, bulk, and nonlinear viscosity are studied. The inflation field energy is represented by a two-components cosmic fluid consisting of a vacuum fluid and a Zel'dovich fluid. It is shown that there exist models in which the viscous Zel'dovich fluid removes the initial singularity of the corresponding viscosity free models. The mean expansion of a Zel'dovich dominated unvierse is found to be independent of shear viscosity and anisotropy. Bulk viscosity and shear viscosity cause exponential decay of anisotropy, while nonlinear viscosity causes power-law decay of anisotropy.     

Bianchi type-V anisotropic cosmological models in certain theories of gravitation with perfect fluid distribution

Exact Bianchi type-V cosmological models are presented in Einstein’s theory of gravitation with cosmological constant Λ in case of perfect fluid distribution. Also obtained Bianchi type-V cosmological models in a scalar-tensor theory of gravitation proposed by Saez and Ballester (1986) in case of perfect fluid distribution using and without using negative constant deceleration parameter. Some physical and geometrical properties of the models are also discussed.     

Cosmological viscous fluid universe in slow rotation

The problem of slowly rotating cosmological viscous fluid universe in a homogeneous and isotropic models has been investigated by considering the perturbation in the metric rotation function to the first order of smallness associated with certain physical restrictions imposed on the metric rotation function and matter angular velocity. Some more general solutions for the metric rotation function have been obtained and physical interpretation of the solutions have been investigated.     

Bulk viscous cosmological models of universe with variable deceleration parameter in Lyra’s Manifold

FRW models of universe in the presence of viscous fluid are investigated in the cosmological theory based on Lyra’s Manifold. By considering the deceleration parameter to be a variable and the viscosity coefficient of bulk viscous fluid to be a constant, exacts solutions have been obtained from which three forms of model of the universe are derived. The physical properties of the models are also investigated.     

Higher Dimensional Cosmological Implications Of A Decay Law For λ Term: Expressions For Some Observable Quantities

Implications of cosmological model with a cosmological term of the form , where β is a constant, are analyzed in multidimensional space time. The proper distance, the luminosity distance-redshift, the angular diameter distance-redshift, and look back time-redshift for the model are presented. It has been shown that models are found to be compatible with the present observations. This work, has thus generalized to higher dimensions the well-known result in four dimensional space time. It is found that the difference is significant at least in the principal to the anologous situation in four dimensional space time.     

Inhomogeneous cosmological models in the presence of massless scalar fields

Non-static inhomogeneous cosmological models are obtained in general relativity for the case of a plane symmetric massless scalar field with cosmological constant A,when the source of the gravitational field is a viscous fluid.Some physical and geometrical behaviors of the solutions are also discussed.     

Bianchi Type I Bulk Viscous Stiff Fluid Tilted Cosmological Model in General Relativity

Bianchi Type I Bulk viscous fluid tilted cosmological model without shearviscosity is investigated. The behaviour of the model in presence andabsence of bulk viscosity is discussed. The physical and geometricalconsequences of the models are also discussed.