Cosmological constant in the Bianchi type-I-modified Brans-Dicke cosmology

In 1961, Brans and Dicke [1] provided an interesting alternative to general relativity based on Mach’s principle. To understand the reasons leading to their field equations, we first consider homogeneous and isotropic cosmological models in the Brans-Dicke theory. Accordingly we start with the Robertson-Walker line element and the energy tensor of a perfect fluid. The scalar field φ is now a function of the cosmic time only. Then we consider spatially homogeneous and anisotropic Bianchi type-I-cosmological solutions of modified Brans-Dicke theory containing barotropic fluid. These have been obtained by imposing a condition on the cosmological parameter Λ(φ). Again we try to focus the meaning of this cosmological term and to relate it to the time coordinate which gives us a collapse singularity or the initial singularity. On the other hand, our solution is a generalization of the solution found by Singh and Singh [2]. As far as we are aware, such solution has not been given earlier.     

Bianchi type-I cosmology in f(R,T) gravity

We investigate the exact solutions of a Bianchi type-I space-time in the context of f(R, T) gravity [1], where f(R, T) is an arbitrary function of the Ricci scalar R and the trace of the energy-momentum tensor T. For this purpose, we find two exact solutions using the assumption of a constant deceleration parameter and the variation law of the Hubble parameter. The obtained solutions correspond to two different models of the Universe. The physical behavior of these models is also discussed.     

The cosmological term and a modified Brans-Dicke cosmology

Adding the cosmological term , which is assumed to be variable in this paper, to the Brans-Dicke Lagrangian, we try to understand the meaning of the term and to relate it to the mass of the universe. We also touch upon the Dirac large-number hypothesis, applying the results obtained from the application of our theory to a uniform cosmological model.     

Some exact solutions in Bianchi VI0 string cosmology

Following the techniques used by Letelier and Stachel some new physically relevant explicit Bianchi VI₀ solutions of string cosmology with magnetic field are reported. They include two models describing distributions of Takabayashi strings and geometric strings respectively.     

Absence of preclassical solutions in Bianchi I loop quantum cosmology

Loop quantum cosmology, the symmetry reduction of quantum geometry for the study of various cosmological situations, leads to a difference equation for its quantum evolution equation. To ensure that solutions of this equation act in the expected classical manner far from singularities, additional restrictions are imposed on the solution. In this Letter, we consider the Bianchi I model, both the vacuum case and the addition of a cosmological constant, and show using generating function techniques that only the zero solution satisfies these constraints. This implies either that there are technical difficulties with the current method of quantizing the evolution equation, or else loop quantum gravity imposes strong restrictions on the physically allowed solutions.     

Some exact solutions of string cosmology in Bianchi III space-time

Following the techniques used by Letelier and Stachel some exact Bianchi III cosmological solutions of massive strings in the presence of magnetic field are obtained and their physical features are discussed. Some string solutions in which magnetic fields are absent are also discussed.     

Whitrow-Randall's relation and Brans-Dicke cosmology

When Brans and Dicke published their alternative gravitational framework, they proved that it led to Machian solutions in the static case, and for a pressureless (dust) Euclidean universe. We extend their demonstration to Euclidean and non-Euclidean models with non-null pressure, employing the perfect fluid model. We find andp both G.     

Bianchi type-I,V and VIo models in modified generalized scalar-tensor theory

In modified generalized scalar-tensor (GST) theory, the cosmological term Λ is a function of the scalar field ϕ and its derivatives . We obtain exact solutions of the field equations in Bianchi Type-I, V and VIo space-times. The evolution of the scale factor, the scalar field and the cosmological term has been discussed. The Bianchi Type-I model has been discussed in detail. Further, Bianchi Type-V and VIo models can be studied on the lines similar to Bianchi Type-I model.      

Brans-Dicke cosmology with time-dependent cosmological term

Berman and Som's solution for a Brans-Dicke cosmology with time-dependent cosmological term, Robertson-Walker metric, perfect fluid, and perfect gas law of state solves the horizon, homogeneity, and isotropy problems without requiring any unnatural fine tuning in the very early universe, thus being an alternative model to inflation. The model also does not need recourse to quantum cosmology, and solves the flatness and magnetic monopole problems.     

Isotropic Brans-Dicke cosmology with dust distribution

A simple approach for finding the exact solution of the matter dust distribution in the Brans-Dicke cosmology has been attempted. The condition for obtaining a complete exact solution is presented.     

Whitrow-Randall's relation and Brans-Dicke cosmology re-visited

The homogeneous and isotropic Brans-Dicke cosmological solutions satisfying Whitrow-Randall's relation which have been discussed recently by Berman and Som are re-examined. After correcting an error in their work, we extend their results and present the most general solution by solving a differential equation completely. We show that Mach's assumption leads to power-law solutions in the Euclidean case.     

Unified regularization of Bianchi cosmology

The Einstein equations for a perfect fluid filled spatially homogeneous space-time are expressed in a reduced form which is as close as possible to a compactified regularized first order system of differential equations, while still respecting both the scale invariance and spatial gauge symmetry of those equations. The present work is a generalization to all Bianchi types of the regularization procedure introduced by Rosquist for Bianchi types III and VI. Jantzen's unified Lie algebra automorphism formalism is used to reduce the gravitational phase space to a subspace parametrized by a minimal number of variables. Although motivated by the qualitative theory of differential equations, the reduced spatially homogeneous Einstein system has also proved useful in the search for new exact solutions.     

毕安基I型宇宙中的混沌

我们研究了在毕安基I型宇宙背景下（Yang-Mills）YM场的动力学演化。我们发现YM场的长时演化对初始条件具有高度的敏感性，即：对系统的固定哈密顿量下初始条件的微小涨落引起场量的迅速变化。通过利用彭加勒截面方法，我们进一步地证明了在毕安基I型宇宙背景下YM场的演化具有典型的混沌特点。     

Bianchi V imperfect fluid cosmology

Bianchi V, spatially homogeneous imperfect fluid cosmological models which contain both viscosity and heat flow are investigated. The Einstein field equations are established in the case that the equations of state are given byp-(-1),=o ^m, and=o ⁿ (where, o, o,m andn are constants). The physical constraints on the solutions of the Einstein field equations, and, in particular, the thermodynamical laws and energy conditions that govern such solutions, are discussed in some detail. Simple power law solutions and solutions in which there is no heat conduction are studied first. Exact solutions are then investigated in more generality, and it is shown that there exist two first integrals of the field equations for certain values of the physical parameters, m andn. Finally, it is shown that in a special case of interest (in whichm =n = 1/2) the imperfect fluid Bianchi V field equations can be written as a plane-autonomous system, thus facilitating the qualitative analysis of these cosmological models.     

Spinor fields in Bianchi type-I universe

A system of minimally coupled nonlinear spinor and scalar fields within the scope of a Bianchi type-I (BI) cosmological model in the presence of a perfect fluid and a cosmological constant (Λ term) is studied, and solutions to the corresponding field equations are obtained. The problem of initial singularity and the asymptotical isotropization process of the Universe are thoroughly studied. The effect of the Λ term on the character of evolution is analyzed. It is shown that some special choice of spinor field nonlinearity generates a regular solution, but the absence of singularity results in violating the dominant energy condition in the Hawking-Penrose theorem. It is also shown that a positive Λ, which denotes an additional gravitational force in our case, gives rise to an oscillatory or a non-periodic mode of expansion of the Universe depending on the choice of problem parameter. The regular oscillatory mode of expansion violets the dominant energy condition if the spinor field nonlinearity occurs as a result of self-action, whereas, in the case of a linear spinor field or nonlinear one that occurs due to interaction with a scalar field, the dominant condition remains unbroken. A system with time-varying gravitational (G) and cosmological (Λ) constants is also studied to some extent. The introduction of magneto-fluid in the system generates nonhomogeneity in the energy-momentum tensor and can be exactly solved only under some additional condition. Though in this case, we indeed deal with all four known fields, i.e., spinor, scalar, electromagnetic, and gravitational, the over-all picture of evolution remains unchanged.