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.     

Tilted Bianchi Type I Cosmological Models for Barotropic Perfect Fluid in General Relativity

In this paper, we have investigated that tilted Bianchi Type I cosmological models for stiff perfect fluid under a supplementary condition A = B ⁿ between metric potentials, is not possible. The tilted solution is also not possible when we assume A = t ^ℓ, B = t ^m , C = t ⁿ ; ℓ, m and n are constants for ε = p. Thus to preserve tilted nature of model, we assume p = γε, 0 ≤ γ ≤ 1 (barotropic equation of state) for the case A = t ^ℓ B = t ^m and C = t ⁿ . The 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.     

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.     

Two-fluid cosmological models in a Bianchi type I space-times

In this paper we present anisotropic, homogeneous two-fluid cosmological models in a Bianchi I space-time. These classes of cosmological models picture two different scenarios of cosmic history; viz., when the radiation and matter content of the universe are in interactive phase and another when the two are non-interacting. The universe is highly anisotropic in the initial stages, however, anisotropy tapers out to insignificance in due course of cosmic evolution. In every model the anisotropy of the space-time is determined by the density parameter Ω₀ at the present epoch. For Ω₀=1, the anisotropy is washed out before long. An interesting class of models, having an inflationary epoch in finite future, is discovered.      

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.     

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.     

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.     

Anisotropic Cosmological Models with a Perfect Fluid and a Λ Term

We consider a self-consistent system of Bianchi type-I (BI) gravitational field and a binary mixture of perfect fluid and dark energy given by a cosmological constant. The perfect fluid is chosen to be the one obeying either the usual equation of state, i.e., p = ζ, with ζ ∊ [0, 1] or a van der Waals equation of state. Role of the Λ term in the evolution of the BI Universe has been studied.     

Bianchi type I cosmological model with variable Λ-term

Bianchi type I perfect fluid cosmological model is investigated with a variable cosmological term. Einstein’s field equations are solved for any arbitrary cosmic scale factor. The main result of the study is the expression for cosmological term as a power law of scale factor. The age of the universe can also be readily calculated.     

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.     

Interacting Scalar And Spinor Fields In Bianchi Type I Universe Filled With Magneto-Fluid

Self-consistent system of spinor, scalar and BI gravitational fields in presence of magneto-fluid and Λ term is considered. Assuming that the expansion of the BI universe is proportional to the σ₁ component of the shear tensor, exact solutions for the metric functions, as well as for scalar and spinor fields are obtained. For a non-positive Λ, the initially anisotropic space–time becomes isotropic one in the process of expansion; whereas for Λ > 0, an oscillatory mode of expansion of the BI model occurs. PACS numbers: 03.65.Pm and 04.20.Ha     

Bianchi Type I Magnetized String Cosmological Model in General Relativity

Bianchi Type I magnetized string cosmological model following the techniques used by Letelier and Stachel, is investigated. To get a determinate model, we assume a condition ∊ = λ (geometric string) where ∊ is the rest energy density, λ the string tension density and expansion (θ) is proportional to eigen value σ₁ ¹ of shear tensor (σ _j ⁱ ), which leads to A = ℓ (BC) ⁿ where A, B, C are metric potentials and ℓ and n are constants. The behaviour of the model in presence and absence of magnetic field is discussed. The physical and geometrical aspects of the model are also discussed.     

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.     

Five dimensional universe model with variable cosmological term Λ and a big bounce

We assume the four dimensional induced matter of the 5D Ricci flat bouncing cosmological solution contains a perfect fluid. The big bounce singularity of simple 5D cosmological model is studied with the cosmological term Λ=α ρ and Λ=β H ² where α and β are constants and ρ and H are respectively energy density and Hubble parameter. This big bounce singularity is found to be an event horizon at which the scale factor and mass density of the universe are finite, while the pressure is infinite.      

Bianchi Type I string dust cosmological model with magnetic field in general relativity

Bianchi Type I string dust cosmological models in presence and absence of magnetic field following the techniques used by Letelier and Stachel, are investigated. To get the deterministic solution, we have assumed that σ ₁¹ is proportional to the expansion (θ) where σ ₁¹ is the eigen value of shear tensor (σ _i ^j ) and which leads to A=N(BC)⁻ⁿ , n>0 where A,B,C are metric potentials and , N and ℓ are constants. The behaviour of the models in presence and absence of magnetic field are discussed. The other physical and geometrical aspects of the model are also discussed.     

Nonlinear spinor field in Bianchi type-I Universe filled with viscous fluid: numerical solutions

We consider a system of nonlinear spinor and a Bianchi type I gravitational fields in presence of viscous fluid. The nonlinear term in the spinor field Lagrangian is chosen to be λ F, with λ being a self-coupling constant and F being a function of the invariants I an J constructed from bilinear spinor forms S and P. Self-consistent solutions to the spinor and BI gravitational field equations are obtained in terms of τ, where τ is the volume scale of BI universe. System of equations for τ and ε, where ε is the energy of the viscous fluid, is deduced. This system is solved numerically for some special cases.      

Bianchi type-V cosmological model with perfect fluid using negative constant deceleration parameter in a scalar tensor theory based on Lyra Manifold

An exact Bianchi type-V perfect fluid cosmological model is obtained in a scalar tensor theory proposed by Sen (Z. Phys. 149:311, 1957) based on Lyra Manifold in case of β is a constant and it is shown that this cosmological model exists only in the case of Radiation Universe (ρ=3p) if β is a function of ‘t’ using negative constant deceleration parameter. Some physical and geometrical properties of these models are discussed.