Bianchi type-I cosmological models with perfect fluid in general relativity

Einstein's field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-Ⅰ universe by assuming that the cosmological term is proportional to R-m(R is a scale factor and m is a constant).A variety of solutions are presented.The physical significance of the respective cosmological models are also discussed.     

Some new Bianchi type-I perfect fluid solutions

We present a simple method to construct some new perfect fluid solutions from known Bianchi type-I solutions.     

Bianchi type-I cosmological models for binary mixture of perfect fluid and dark energy

We consider a self consistent system of Bianchi Type-I cosmology and Binary Mixture of perfect fluid and dark energy. The perfect fluid is taken to be obeying equations of state p _PF =γρ _PF with γ∈[0,1]. The dark energy is considered to be obeying a quintessence-like equation of state where the dark energy obeys equation of state p _DE =ωρ _DE where ω∈[−1,0]. Exact solutions to the corresponding Einstein field equations are obtained. Some special cases are discussed and studied. Further more power law models and exponential models are investigated.     

Bianchi type-V cosmological models with perfect fluid and dark energy

We consider a self-consistent system of Bianchi type-V 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=γ ρ with γ∈[0,1]. The dark energy is considered to be either the quintessence or Chaplygin gas. Exact solutions to the corresponding Einstein equations are obtained as a quadrature. The cases of disordered radiation and models with power-law and exponential expansion have discussed in detail. For large t, the models tend to be isotropic.     

Inhomogeneous generalizations of Bianchi type VIh models with perfect fluid

Inhomogeneous universes admitting an AbelianG ₂ of isometry and filled with perfect fluid have been derived. These contain as special cases exact homogeneous universes of Bianchi type VI_h.Many of these universes asymptotically tend to homogeneous Bianchi VI_h universes. The models have been discussed for their physical and kinematical behaviours.     

Bianchi type-I cosmological effective stiff fluid model in Saez and Ballester theory

The problem of viscous fluid distribution in Bianchi type I space-time is considered here in a new scalar tensor theory of gravitation proposed by Saez and Ballester (1986). Particular solutions of the field equations are derived assuming the viscous coefficient to be the power functions of energy density. Some physical and geometrical properties of the solutions are also discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Bianchi type-VI0 perfect fluid cosmological models with magnetic field

In this paper we discuss Bianchi type-VI₀ cosmological models with perfect fluid distribution and magnetic field directed along the axial direction. Einstein's equations have been solved for the condition that the expansion scalar bears a constant ratio to the anisotropy in the direction of a space-like unit vector ⁱ.     

Anisotropic Bianchi type-I models in string cosmology

The present study deals with a spatially homogeneous and anisotropic Bianchi-I cosmological models representing massive strings. The energy-momentum tensor, as formulated by Letelier (1983), has been used to construct massive string cosmological models for which we assume the expansion scalar in the models is proportional to one of the components of shear tensor. The Einstein’s field equations have been solved by applying a variation law for generalized Hubble’s parameter in Bianchi-I space-time. We have analysed a comparative study of accelerating and decelerating models in the presence of string scenario. The study reveals that massive strings dominate in the decelerating universe whereas strings dominate in the accelerating universe. The strings eventually disappear from the universe for sufficiently large times, which is in agreement with current astronomical observations.     

Bianchi type-I models in self-creation theory of gravitation

Spatially-homogeneous and anisotropic Bianchi type-I cosmological models are obtained, in Barber's second self-creation theory of gravitation, when the source of the gravitational field is a perfect fluid. Some physical and geometrical properties of the models are discussed.     

Bianchi type-VI0 perfect fluid cosmological model in a modified theory of gravity

A spatially homogeneous and anisotropic Bianchi type-VI₀ space-time filled with perfect fluid in general relativity and also in the framework of f(R,T) gravity proposed by Harko et al. (in arXiv:1104.2669 [gr-qc], 2011) has been studied with an appropriate choice of the function f(R,T). The field equations have been solved by using the anisotropy feature of the universe in Bianchi type-VI₀ space time. Some important features of the models, thus obtained, have been discussed. We noticed that the involvement of new function f(R,T) doesn’t affect the geometry of the space-time but slightly changes the matter distribution.     

Bianchi type I cosmological perfect fluid model in scale invariant theory

The intention of this paper is to study the perfect fluid distribution in scale invariant theory of gravity when the space-time is described by Bianchi type I metric with a time dependent gauge function. The cosmological equations for this space-time with gauge function are solved and some physical properties of the model are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bianchi type-I vacuum model in self-creation cosmology

A simple and elegant generalisation of the Kasner model is presented in a self-creation theory of gravitation, proposed by Barber by solving the field equations corresponding to the Bianchi type-I metric. Some physical properties of the model are discussed.     

Bianchi type-VI0 and type-VIh perfect fluid solutions

We present a consistent method to construct some new Bianchi type-VI₀ and type-VI_h perfect fluid solutions from known solutions. The corresponding seed solutions are due to Collins (1971).     

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.     

de Sitter expansion with anisotropic fluid in Bianchi type-I space-time

Some features of the Bianchi type-I universes in the presence of a fluid that wields an anisotropic equation of state (EoS) parameter are discussed in the context of general relativity. The models that exhibit de Sitter volumetric expansion due to the constant effective energy density (the sum of the energy density of the fluid and the anisotropy energy density) are of particular interest. We also introduce two locally rotationally symmetric models, which exhibit de Sitter volumetric expansion in the presence of a hypothetical fluid that has been obtained by minimally altering the conventional vacuum energy. In the first model, the directional EoS parameter on the x axis is assumed to be −1, while the ones on the other axes and the energy density of the fluid are allowed to be functions of time. In the second model, the energy density of the fluid is assumed to be constant, while the directional EoS parameters are allowed to be functions of time.     

Inhomogeneous generalisation of Bianchi type-VIo cosmological model of perfect fluid distribution in general relativity

Einstein's equations have been solved for perfect fluid distribution. The solution obtained may be considered as inhomogeneous generalisation of Bianchi type-VI_o cosmological model.     

Anisotropic Bianchi type-I models with constant deceleration parameter in general relativity

A special law of variation for Hubble’s parameter is presented in a spatially homogeneous and anisotropic Bianchi type-I space-time that yields a constant value of deceleration parameter. Using the law of variation for Hubble’s parameter, exact solutions of Einstein’s field equations are obtained for Bianchi-I space-time filled with perfect fluid in two different cases where the universe exhibits power-law and exponential expansion. It is found that the solutions are consistent with the recent observations of type Ia supernovae. A detailed study of physical and kinematical properties of the models is carried out.     

Bianchi type-II, VIII & IX perfect fluid magnetized cosmological models in Brans-Dicke theory of gravitation

Spatially homogeneous Bianchi type-II, VIII & IX charged perfect fluid cosmological models in Brans-Dicke theory of gravitation are obtained and presented. Various physical and geometrical features of the models are also discussed.