Early inflation,isotropization, and late time acceleration in a Bianchi type-I universe

A system of Einstein equations is solved for the Bianchi type-I metrics that describes a homogeneous and isotropic Universe. The system contains nonlinear differential equations of the second-order, which depend only on time. The method of solution is described, and the general form of the solution is found. Explicit analytical expressions are obtained in some particular cases. Numerical integration is used to describe possible solution types in the general case. The evolution of the Universe has been investigated in the presence of different types of sources, namely, a perfect fluid, a van der Waals fluid, the cosmological constant, quintessence, a Chaplygin gas, a modified quintessence, and a nonlinear spinor field. It is shown that the presence of a van der Waals fluid leads to inflation in the early stage of evolution, while the modified quintessence leads to a cyclic or oscillating Universe. It has been shown, that for some special choice of parameters the late time acceleration can be attributed to the influence of a nonlinear spinor field.     

Nonlinear Spinor Fields in Bianchi type-III Spacetime

Within the scope of Bianchi type-III spacetime we study the role of spinor field on the evolution of the Universe as well as the influence of gravity on the spinor field. In doing so we have considered a polynomial type of nonlinearity. In this case the spacetime remains locally rotationally symmetric and anisotropic all the time. It is found that depending on the sign of nonlinearity the models allows both accelerated and oscillatory modes of expansion. The non-diagonal components of energy-momentum tensor though impose some restrictions on metric functions and components of spinor field, unlike Bianchi type I, V and V I ₀ cases, they do not lead to vanishing mass and nonlinear terms of the spinor field.     

Nonlinear Spinor Fields in Bianchi Type-I Spacetime Reexamined

The specific behavior of spinor field in curve space-time with the exception of FRW model almost always gives rise to non-trivial non-diagonal components of the energy-momentum tensor. This non-triviality of non-diagonal components of the energy-momentum tensor imposes some severe restrictions either on the spinor field or on the metric functions. In this paper within the scope of an anisotropic Bianchi type-I Universe we study the role of spinor field in the evolution of the Universe. It is found that there exist two possibilities. In one scenario the initially anisotropic Universe evolves into an isotropic one asymptotically, but in this case the spinor field itself undergoes some severe restrictions. In the second scenario the isotropization takes places almost at the beginning of the process.     

Bianchi type-I solutions for modified Brans-Dicke cosmology

Cosmological dust solutions have been obtained in Bianchi type-I homogeneous space for Brans-Dicke modified theory by the condition of the cosmological parameter ().     

A higher-dimensional Bianchi type-I inflationary Universe in general relativity

A five-dimensional Bianchi type-I inflationary Universe is investigated in the presence of massless scalar field with a flat potential. To get an inflationary Universe, a flat region in which the potential V is constant is considered. Some physical and kinematical properties of the Universe are also discussed.     

Bianchi type I inflationary universe in general relativity

In this paper, we have investigated Bianchi type I inflationary universe in the presence of massless scalar field with a flat potential. To get an inflationary solution, we have considered a flat region in which potential V is constant. The inflationary scenario of the model is discussed in detail.     

Spinor fields in non-abelian Klein-Kaluza theories

We introduce a dimensional reduction procedure for a spinor field and a generalization of the minimal coupling scheme. We get an electric dipole moment of fermions of value 10^–31 cm and PC breaking for a gauge groupG with odd parameters. Reflection in higher (additional) dimensions are proposed as a conjugation of color charges connected with Yang-Mills fields. Our approach cancels Planck's mass terms in the Dirac equation.     

Spinor fields at spacelike infinity

The concept of a spinor structure at spacelike infinity is introduced for space-times which are asymptotically flat. It is shown how zero-rest-mass fields on space-time acquire smooth limits on this structure and that these limits satisfy certain differential equations characterized by the helicity and regularity of the field. The geometry of the limits of twistor fields is also discussed, and it seems possible that one can define the momentum and angular momentum of an asymptotically flat space-time in terms of a twistor space at spacelike infinity.     

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.     

Scalar field cosmologies in a Bianchi type I universe

The dynamics of a homogeneous, anisotropic, spatially flat Bianchi type I universe filled with a scalar field is studied. Using the usual synchronous form of the line element, general exact solutions for the Einstein field equations are obtained in the case of the exponential-potential scalar field (V=Λexp(k?)) and in the case of the Barrow-Saich potential ( $V \sim \dot \varphi ^2 $ ). Conditions under which inflation can occur are discussed and the late-time behaviour of the models is also considered.     

Quantum stationary state of class A Bianchi universe

Padmanabhan derived a differential equation for the stationary state for the class A Bianchi model and obtained some approximate solutions. Here we reduce the differential equation to a standard, well-known, solvable linear differential equation and indicate some exact explicit particular solutions.     

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.     

Spinor fields and symmetries of the spacetime

We show that in the background of a stationary and axisymmetric black hole, there is a particular spinor field whose “conserved current” interpolates between the null Killing vector on the horizon and the time Killing vector at the spatial infinity. The spinor field only needs to satisfy a very general and simple constraint.     

Spinor and electromagnetic fields in space with torsion

A combined system of Einstein-Cartan, Ivanenko-Heisenberg, and Maxwell equations is reduced to a combined system of Einstein, Dirac, and Maxwell equations in Riemann space. A solution in which metric singularities are absent is found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 31–35, November, 1978.     

A new class of LRS Bianchi type-I cosmological models in Lyra geometry

LRS Bianchi type-I models have been studied in the cosmological theory based on Lyra’s geometry. A new class of exact solutions has been obtained by considering a time dependent displacement field for constant deceleration parameter models of the universe. The physical behaviour of the models is examined in vacuum and in the presence of perfect fluids.