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.     

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.     

Bianchi Type V Barotropic Perfect Fluid Cosmological Model in Lyra Geometry

We have investigated Bianchi Type V barotropic perfect fluid cosmological model in Lyra geometry. To get the deterministic model of the universe, we have assumed the barotropic perfect fluid condition p=γ ρ, 0≤γ≤1 and energy conservation equation i.e. T _i;j ^j =0. The physical and geometrical aspects of the model are discussed. The special cases for γ=1 (stiff fluid distribution), γ=0 (dust distribution), γ=1/3 (disordered radiation) are also discussed.     

Ricci Collineations in Perfect Fluid Bianchi V Spacetime

The Bianchi V spacetimes with perfect-fluid matter are classified according to their Ricci collineations. We have found that in the degenerate case there are infinitely many Ricci collineations whereas a subcase gives a finite number of Ricci collineations which are five. In the non-degenerate case the group of Ricci collineations is finite, i.e. four or five or six or seven. Also, all results obtained satisfy the energy conditions.     

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.     

Assisted Inflation in Bianchi VI0 Cosmologies

Exact models for Bianchi VI₀ spacetimes with multiple scalar fields with exponential potentials have been derived and analysed. It has been shown that these solutions, when they exist, attract neighbouring solutions in the two cases corresponding to interacting and non-interacting fields. Unlike the results obtained in a previous work dealing with the late-time inflationary behaviour of Bianchi VI₀ cosmologies, the knowledge of exact solutions has made possible to study in detail the occurrence of inflation before the asymptotic regime. As happened in preceding works, here as well inflation is more likely to happen with a higher number of non-interacting fields or a lower number of interacting scalar fields.     

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 V Magnetized String Dust Bulk Viscous Fluid Cosmological Model with Variable Magnetic Permeability

Bianchi Type V magnetized string dust bulk viscous fluid cosmological model with variable magnetic permeability, is investigated. The magnetic field is due to an electric current produced along x-axis. Thus the magnetic fields is in yz-plane and F ₂₃ is the only non-vanishing component of electromagnetic field tensor F _ij . To get the deterministic model in terms of cosmic time t, we have also assumed the condition ζ θ=constant where ζ the coefficient of bulk viscosity and θ the expansion in the model. The behaviour of the model in presence and absence of magnetic field and bulk viscosity and singularities in the model are also discussed.      

Bianchi Type I String Dust Magnetized Cosmological Models in Lyra Geometry

Bianchi type I string dust cosmological models in the presence and absence of magnetic field in the frame work of Lyra geometry are investigated. To get the deterministic model of the universe, we assume that the eigenvalue （σ^11） of shear tensor （σ^ii） is proportional to expansion （θ）. This leads to A = （BC）^n, where A, B, C are metric potentials and n is a constant. To discuss the results in terms of cosmic time t, we have considered n = 1. The physical and geometrical aspects＇ of the models and singularities in the models are also discussed.     

Bianchi Type I String Dust Magnetized Cosmological Models in Lyra Geometry

Bianchi type I string dust cosmological models in the presence and absence of magnetic field in the frame work of Lyra geometry are investigated. To get the deterministic model of the universe, we assume that the eigenvalue (σ₁¹ ) of shear tensor (σ_i ^j ) is proportional to expansion (θ ). This leads to A =(BC)ⁿ, where A, B, C are metric potentials and n is a constant. To discuss the results in terms of cosmic time t, we have considered n = 1. The physical and geometrical aspects of the models and singularities in the models are also 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.     

Bianchi Type Ⅲ String Cosmological Model with Bulk Viscosity

The Bianchi type Ⅲ cosmological model for a cloud string with bulk viscosity are presented. To obtain a determinate model, an equation of state ρ=kλ and a relation between metric potentials B = C^n are assumed. The physical and geometric aspects of the model are also discussed. The model describes a shearing non-rotating continuously expanding universe with a big-bang start, and the relation between the coefficient of bulk viscosity and the energy density is ζ∝ρ^1/2.     

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 VI String Cosmological Model in Saez–Ballester’s Scalar-Tensor Theory of Gravitation

An exact Bianchi type-VI string cosmological model is obtained in a scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. 113:467, 1985). Some physical properties of the model are also discussed.     

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.     

Energy Conditions and Conservation Laws in LRS Bianchi Type I Spacetimes via Noether Symmetries

In this paper, we have completely classified the locally rotationally symmetric (LRS) Bianchi type I spacetimes via Noether symmetries (NS). The usual Lagrangian corresponding to LRS Bianchi type I metric is used to find the set of determining equations. To achieve a complete classification, these determining equations are generally integrated to find the components of NS vector field and the metric coefficients. During this procedure, several cases arise which give different Noether algebras of dimension 5,..., 9, 11, and 17. A comparison is established between the obtained NS and the Killing and homothetic vectors. Corresponding to all NS generators, the conservation laws are stated by using Noether's theorem. The metrics which we have obtained as a result of our classification are shown to be anisotropic or perfect fluids which satisfy certain energy conditions.     

Interacting Spinor and Scalar Fields in Bianchi Type I Universe Filled with Perfect Fluid: Exact Self-Consistent Solutions

In the framework of Bianchi I (BI) cosmological models a self-consistent system of interacting spinor and scalar fields has been considered. We introduced an interaction function F(I, J) which is an arbitrary function of invariants I and J, generated from the real bilinear forms of the spinor field. Exact self-consistent solutions to the field equations have been obtained for the cosmological model filled with perfect fluid. The initial and the asymptotic behavior of the field functions and of the metric one has been thoroughly studied.     

Bianchi Type <Emphasis Type="Italic">VI</Emphasis><Subscript>0</Subscript> Magnetized Barotropic Bulk Viscous Fluid Massive String Universe in General Relativity

A model of a cloud formed by massive strings is studied in the context of the usual general relativity. This model is used as a source of Bianchi type VI ₀ massive with magnetic field and bulk viscosity. To get a determinate model, we assume that the expansion (θ) in the model is proportional to the shear (σ) and also the fluid obeys the barotropic equation of state. The behaviour of the models from physical and geometrical aspects in presence and absence of magnetic field and bulk viscosity is discussed.     

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.     

Bianchi type IX asymptotical behaviours with a massive scalar field: chaos strikes back

We use numerical integrations to study the asymptotical behaviour of a homogeneous but anisotropic Bianchi type IX model in General Relativity with a massive scalar field. As it is well known, for a Brans-Dicke theory, the asymptotical behaviour of the metric functions is ruled only by the Brans-Dicke coupling constant ₀ with respect to the value –3/2. In this paper we examine if such a condition still exists with a massive scalar field. We also show that, contrary to what occurs for a massless scalar field, the singularity oscillatory approach may exist in the presence of a massive scalar field having a positive energy density.