Bianchi type-II cosmological model with viscous fluid

A spatially homogeneous and locally rotationally symmetric Bianchi type-II cosmological model under the influence of both shear and bulk viscosity has been studied. Exact solutions are obtained with a barotropic equation of state (p=) and considering the linear relationships between, ², and ², which represent the fluid density, the expansion, and the shear scalars, respectively. Special cases with vanishing bulk viscosity coefficients and with the perfect fluid in the absence of viscosity have also been studied. The formal appearance of the solutions is the same for both the viscous as well as the perfect fluids. The difference is only in choosing a constant parameter which appears in the solutions. In the cases of either a fluid with bulk viscosity alone or a perfect fluid, the barotropic equation of state is no longer an additional assumption to be imposed; rather it follows directly from the field equations.     

Bianchi I cosmological model and the no-boundary condition

A study of the Bianchi I cosmological model is done from both the classical and quantum mechanical points of view. The field equations and their solutions are discussed in the classically forbidden region and classical region. Also the noboundary wave function is evaluated using the concept of microsuperspace and the Hawking-Hartle proposal.     

Bianchi type IX string cosmological model in general relativity

We have investigated Bianchi type IX string cosmological models in general relativity. To get a determinate solution, we have assumed a condition ρ=λ i.e. rest energy density for a cloud of strings is equal to the string tension density. The various physical and geometrical aspects of the models are also discussed.     

Bianchi Type-IX viscous fluid cosmological model in general relativity

Bianchi Type-IX viscous fluid cosmological model is investigated. To get a deterministic model, we have assumed the conditiona = b ^m(m is a constant) between metric potentials andη ∞θ whereη is the coefficient of shear viscosity andθ the scalar of expansion in the model. The coefficient of bulk viscosity (ς) is taken as constant. The physical and geometrical aspects of the model are also discussed.     

Geodesic Bianchi type cosmological models

Some perfect fluid solutions of Einstein's field equations are obtained in spacetimes with two hypersurface orthogonal space-lika commuting Killing vectors. The flow is assumed to be geodesic. The solutions depend on an arbitrary function of time which determines the equation of state. In the models derived one additional Killing vector exists and the solutions are actually Bianchi-type cosmological models.     

The Bianchi IX cosmological models

Two cosmological models for the Bianchi IX metric are constructed. These include the following sources of gravitation: 1) a co-moving anisotropic liquid, non-comoving dust, and a scalar field; 2) an anisotropic liquid, pure radiation, and a scalar field. The kinematic parameters of the models are found.     

Classical and quantum aspects of Bianchi type IX cosmological model

A detailed study of the Bianchi type IX cosmological model is done. Classical field equations are discussed with a massive scalar field. The Wheeler-DeWitt quantum equation is formed and is solved using a Born-Oppenheimer type of approximation.     

Bianchi type I anisotropic cosmological model with a collisionless gas

The self-consistent system of Einstein-Vlasov equations is investigated in a class of homogeneous spaces. The Bianchi Type I anisotropic cosmological model with orthogonal Killing vectors is considered in detail. It is shown that the energymomentum tensor of a collisionless gas is spatially anisotropic. Exact solutions of the Einstein-Vlasov equations are found in the case of strong anisotropy. The behavior of small perturbations is investigated for a mixture of an ideal fluid and a collisionless gas as well as for a nonrelativistic collisionless gas.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 3–8, May, 1981.     

Stationary cosmological Bianchi II solutions

Stationary cosmological solutions for the Bianchi metric II are derived. In the models, use is made of a scalar field with a vacuum-averaged energy-momentum tensor, a cosmological constant, and ideal co-moving or not co-moving liquids as sources of gravitations.     

Tilted Bianchi type I dust fluid cosmological model in general relativity

In this paper, we have investigated a tilted Bianchi type I cosmological model filled with dust of perfect fluid in general relativity. To get a determinate solution, we have assumed a condition A = B ⁿ between metric potentials. The physical and geometrical aspects of the model together with singularity in the model are also discussed.     

Neutrino solution of Dirac equation in Bianchi type V cosmological model

The Dirac equation in Bianchi type V cosmology is established, and neutrino solutions in the early universe are presented.     

Fluctuations produced by the cosmological constant in the empty Bianchi type-IX model

We analyze the fluctuations of the gravitational field, produced by the cosmological term, in the empty Bianchi type-IX cosmological model. It is shown that such fluctuations do not change the process of alternation of Kasner eras very near to the singularity, and that a positive cosmological constant leads to an asymptotic isotropization of the model.     

Bianchi type-II universe with linear equation of state

We have studied anisotropic and homogeneous Bianchi type-II cosmological model with linear equation of state (EoS) p = αρ?β, where α and β are constants, in General Relativity. In order to obtain the solutions of the field equations we have assumed the geometrical restriction that expansion scalar θ is proportional to shear scalar σ. The geometrical and physical aspects of the model are also studied.     

Rotating cosmological models of Bianchi type VIII

We find cosmological solutions with rotation of Bianchi type VIII for the energy-momentum tensor of a perfect fluid with heat flow.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 98–103, May, 1989.In conclusion the author expresses thanks to the participants in Professor D. D. Ivanenko's seminar for helpful discussions.     

Bianchi type-I massive string magnetized barotropic perfect fluid cosmological model in bimetric theory

Bianchi type-I massive string cosmological model for perfect fluid distribution in the presence of magnetic field is investigated in Rosen’s [Gen. Relativ. Gravit. 4, 435 (1973)] bimetric theory of gravitation. To obtain the deterministic model in terms of cosmic time, we have used the condition A = (BC) ⁿ , where n is a constant, between the metric potentials. The magnetic field is due to the electric current produced along the x-axis with infinite electrical conductivity. Some physical and geometrical properties of the exhibited model are discussed and studied.     

Bianchi type-I bulk viscous fluid string dust magnetized cosmological model in general relativity

Bianchi Type-I magnetized bulk viscous fluid string dust cosmological model is investigated. To get a determinate model, we have assumed the conditions σ ∝θ andζθ = constant where σ is the shear,θ the expansion in the model andζ the coefficient of bulk viscosity. 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.     

Bianchi type-V string cosmological models in general relativity

Bianchi type-V string cosmological models in general relativity are investigated. To get the exact solution of Einstein’s field equations, we have taken some scale transformations used by Camci et al [Astrophys. Space Sci. 275, 391 (2001)]. It is shown that Einstein’s field equations are solvable for any arbitrary cosmic scale function. Solutions for particular forms of cosmic scale functions are also obtained. Some physical and geometrical aspects of the models are discussed.