Plane Symmetric Inhomogeneous Cosmological Models with a Perfect Fluid in General Relativity

In this paper we investigate a class of solutions of Einstein equations for the plane- symmetric perfect fluid case with shear and vanishing acceleration. If these solutions have shear, they must necessarily be non-static. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three classes of solutions. PACS No.: 04.20.-q.     

Bianchi Type-IX String Cosmological Models for Perfect Fluid Distribution in General Relativity

The present study deals with Bianchi type-IX string cosmological models for perfect fluid distribution. We consider two cases： （i） ρ ＋ λ = 0, （ii） ρ - λ = 0, where ρ and λ are the rest energy density and the tension density of a string cloud, respectively. The physical and geometrical properties of the models are discussed.     

Bianchi Type I Magnetized Barotropic Perfect Fluid Cosmological Model in General Relativity

Bianchi Type I barotropic perfect fluid cosmological model in presence of magnetic field, is investigated. To get the deterministic model, we have also assumed that σ ₁¹ α θ where σ ₁¹ is the eigen-value of shear tensor σ _i ^j and θ the expansion in the model. The behavior of the model in presence and absence of magnetic field and singularities in the model are also discussed.     

Quantum Cosmological Perfect Fluid Models

Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state p = are constructed using Schutz's variational formalism. In this approach the notion of time can be recovered. By superposition of stationary states, finite-norm wave-packet solutions to the Wheeler-DeWitt equation are found. The behaviour of the scale factor is studied by applying the many-worlds and the ontological interpretations of quantum mechanics. Singularity-free models are obtained for < 1. Accelerated expansion at present requires –1/3 > > – 1.     

Bianchi .Type-I Massive String Magnetized Barotropic Perfect Fluid Cosmological Model in General Relativity

Bianchi type-I massive string cosmological model with magnetic field of barotropic perfect fluid distribution through the techniques used by Latelier and Stachel is investigated. To obtain the deterministic model of the universe, it is assumed that the universe is filled with barotropic perfect fluid distribution. The magnetic field is due to electric current produced Mong the x-axis with infinite electrical conduictivity. The behaviour of the model in the presence and absence of magnetic field together with other physical aspects is further discussed.     

On Average Properties of Inhomogeneous Fluids in General Relativity: Perfect Fluid Cosmologies

For general relativistic spacetimes filled with an irrotational perfect fluid a generalized form of Friedmann's equations governing the expansion factor of spatially averaged portions of inhomogeneous cosmologies is derived. The averaging problem for scalar quantities is condensed into the problem of finding an "effective equation of state" including kinematical as well as dynamical "backreaction" terms that measure the departure from a standard FLRW cosmology. Applications of the averaged models are outlined including radiation-dominated and scalar field cosmologies (inflationary and dilaton/string cosmologies). In particular, the averaged equations show that the averaged scalar curvature must generically change in the course of structure formation, that an averaged inhomogeneous radiation cosmos does not follow the evolution of the standard homogeneous-isotropic model, and that an averaged inhomogeneous perfect fluid features kinematical "backreaction" terms that, in some cases, act like a free scalar field source. The free scalar field (dilaton) itself, modelled by a "stiff" fluid, is singled out as a special inhomogeneous case where the averaged equations assume a simple form.     

Five Dimensional Cosmological Models in General Relativity

A five dimensional Kaluza-Klein space-time is considered in the presence of a perfect fluid source with variable G and Λ. An expanding universe is found by using a relation between the metric potential and an equation of state. The gravitational constant is found to decrease with time as G∼t ^−(1−ω) whereas the variation for the cosmological constant follows as Λ∼t ⁻², L ~ ([(R)\dot]/R)²\Lambda \sim (\dot{R}/R)^{2} and L ~ [(R)\ddot]/R\Lambda \sim \ddot{R}/R where ω is the equation of state parameter and R is the scale factor.     

Two Fluids Tilted Cosmological Models in General Relativity

Tilted homogeneous plane symmetric two fluids cosmological models with matter and radiating source are investigated. In the model one of the fluids represents the matter content of the universe and another fluid is the CMB radiation. The tiltedness is also considered .With the help of variation for Hubble’s parameter proposed by Bermann a cosmological model with negative constant deceleration parameter is obtained. We have also investigated the behaviours of some physical parameters.     

Kasner Cosmological Models with Two-Fluid Source in General Relativity

In this paper we present Bianchi type-I metric of the Kasner form describing two-fluid source of the universe in general relativity. In Kasner cosmological models one fluid is a radiation field modeling the cosmic microwave background, while the other is a matter field, modeling material content of the universe. The radiation and matter content of the universe are in interactive phase. We have also presented anisotropic, homogeneous nature of Kasner cosmological models with two-fluid. The behavior of fluid parameters and kinematical parameters of the models are also discussed.     

Bianchi Type-II Bulk Viscous String Cosmological Models in General Relativity

Some Bianchi type II bulk viscous string cosmological models with electromagnetic field are investigated. To get a determinate solution, we assume the shear (σ) is proportional to the expansion (θ), which leads to a supplementary condition B=lA ⁿ , between metric potentials, is used where A and B are function of time alone. A particular solution for n=0 is also discussed. The physical and geometrical implications of the models are discussed.     

Anisotropic Cosmological Models with Perfect Fluid and Dark Energy Reexamined

We consider a self consistent system of Bianchi type-I (BI) gravitational field and a binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be the one obeying the usual equation of state, i.e., p = ξε, with ζ∉[0, 1] whereas, the dark energy is considered to be obeying a quintessence-like equation of state. The modification of the ordinary quintessence lies in the fact that its pressure becomes positive if the (dark) energy density exceeds some critical value. Exact solutions to the corresponding Einstein equations are obtained. The model in consideration gives rise to a Universe which is spatially finite. Depending on the choice of problem parameters the Universe is either close with a space-time singularity, or an open one which is oscillatory, regular and infinite in time. PACS numbers: 04.20.Ha, 03.65.Pm, 04.20.Jb     

Bianchi Type-III Magnetized Wet Dark Fluid Cosmological Model in General Relativity

Bianchi type-III cosmological model of universe filled with dark energy from a wet dark fluid (WDF) in presence and absence of magnetic field is investigated in general theory of relativity. We assume that F ₁₂ is the only non-vanishing component of F _ij . We obtain exact solutions to the field equations using the condition that expansion is proportional to the shear scalar i.e. (B=C ⁿ ). The physical behavior of the model is discussed with and without magnetic field. We conclude that universe model do not approach isotropy through the evolution of the universe.     

Magnetized Bianchi Type III Massive String Cosmological Models in General Relativity

The present study deals with Bianchi type III string cosmological models with magnetic field. The magnetic field is assumed to be along z direction. Therefore F ₁₂ is only the non-vanishing component of electromagnetic field tensor F _ij . The expansion (θ) in the model is assumed to be proportional to the shear (σ). To get determinate solution in term of cosmic time, we have solved the fields equations in two cases (i) Reddy and (ii) Nambu string. The physical and geometrical behaviour of these models is discussed.     

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.     

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

A plane-symmetric inhomogeneous cosmological model of perfect fluid distribution 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.     

Higher Dimensional Plane Symmetric Cosmological Models with Two-Fluid Source in General Relativity

We consider anisotropic, homogeneous two-fluid plane symmetric cosmological models in higher dimensions. Here one fluid represents the matter content of the universe and another fluid is chosen to model the CMB (cosmic microwave background) radiation. The radiation and matter content of the universe are in interactive phase. Also we have discussed the behaviour of fluid parameters and kinematical parameters.     

Bianchi Type V Cosmological Models with Constant Deceleration Parameter in General Relativity

We investigate Bianchi type V cosmological models with bulk viscous fluid source. Exact solutions of the Einstein field equations are presented via a suitable power law assumption for the Hubble parameter. We show that the corresponding solutions retain the well established features of the standard cosmology and in addition, are in accordance with recent type Ia supernovae observations. Some observational parameters for the models have also been discussed.     

Bulk Viscus Fluid Plane Symmetric String Dust Magnetised Cosmological Model in General Relativity

In this paper we have investigated bulk viscous fluid plane symmetric dust magnetized string cosmological model. To get a deterministic model, it is assumed that ε=λ, and a relation between metric potential B=RA ⁿ . The behaviour of the model in the presence and absence of magnetic field together with physical and geometrical aspects of the model are also discussed.     

Higher Dimensional Bianchi Type-V Cosmological Models with Perfect Fluid and Dark Energy

We have studied the Bianchi type-V cosmological models with binary mixture of perfect fluid and dark energy in five dimensions. The perfect fluid is obeying the equation of state p=γρ with γ∈[0,1]. The dark energy is considered to be either the quintessence or the Chaplygin gas. The exact solutions of the Einstein’s field equations are obtained in quadrature form.     

Bianchi Type VI0 Cosmological Models with Perfect Fluid and Dark Energy

We consider a self-consistent system of Bianchi Type VI₀ cosmology and binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be one obeying the usual equation of state p=??? with ????[0,1]. The dark energy is considered to be either the quintessence or Chaplygin gas. Exact solutions to the corresponding Einstein??s field equations are obtained as a quadrature. Models with power-law and exponential expansion have discussed in detail.