Bianchi Type-III Bulk Viscous and Barotropic Perfect Fluid Cosmological Models in Lyra’s Geometry

We have investigated Bianchi type III bulk viscous and barotropic perfect fluid cosmological models in the frame work of Lyra’s geometry. To get deterministic models of universe, we have assumed the three conditions: (i) shear scalar (σ) is proportional to the expansion (θ). This leads to B=C ⁿ , where B and C are metric potentials. (ii) In presence of viscous fluid, the coefficient of viscosity of dissipative fluid is a power function of mass density ξ=ξ ₀ ρ ^m , where ξ ₀ and m are constant and (iii) in absence of viscosity, a proportionality relation between pressure and energy density of barotropic perfect fluid p=αρ, where α is a proportionality constant. In all the cases, we observed that the displacement vector β is large at beginning of the universe and reduces fast during its evolution so that its nature coincide with the behavior of cosmological constant Λ.     

A New Class of Inhomogeneous Cosmological Models with Electromagnetic Field in Normal Gauge for Lyra’s Manifold

A new class of exact solutions of Einstein’s modified field equations in inhomogeneous space-time for perfect fluid distribution with electromagnetic field is obtained in the context of normal gauge for Lyra’s manifold. We have obtained solutions by considering the time dependent displacement field. The source of the magnetic field is due to an electric current produced along the z-axis. Only F ₁₂ is a non-vanishing component of the electromagnetic field tensor. It has been found that the displacement vector β(t) behaves like the cosmological constant Λ in the normal gauge treatment and the solutions are consistent with the recent observations of Type Ia supernovae. Physical and geometric aspects of the models are also discussed in the presence of magnetic field.     

LRS Bianchi Type II Perfect Fluid Cosmological Models in Normal Gauge for Lyra’s Manifold

The present study deals with spatially homogeneous and locally rotationally symmetric (LRS) Bianchi type II cosmological models of perfect fluid distribution of matter for the field equations in normal gauge for Lyra’s manifold where gauge function β is taken as time dependent. To get the deterministic models of the universe, we assume that the expansion (θ) in the model is proportional to the shear (σ). This leads to condition R=mS ⁿ , where R and S are metric potentials, m and n are constants. We have obtained two types of models of the universe for two different values of n. It has been found that the displacement vector β behaves like cosmological term Λ in the normal gauge treatment and the solutions are consistent with recent observations. Some physical and geometric behavior of these models are also discussed.     

Anisotropic Bianchi Type-I String Cosmological Models in Normal Gauge for Lyra’s Manifold with Constant Deceleration Parameter

The present study deals with a spatially homogeneous and anisotropic Bianchi type-I (B-I) cosmological models representing massive strings in normal gauge for Lyra’s manifold by applying the variation law for generalized Hubble’s parameter that yields a constant value of deceleration parameter. The variation law for Hubble’s parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential-law type. Using these two forms, Einstein’s modified field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The energy-momentum tensor for such string as formulated by Letelier, P.S.: Phys. Rev. D 28, 2414 (1983) is used to construct massive string cosmological models for which we assume that the expansion (θ) in the model is proportional to the component s¹ ₁\sigma^{1}_{~1} of the shear tensor s^j _i\sigma^{j}_{~i}. This condition leads to A=(BC) ^m , where A, B and C are the metric coefficients and m is proportionality constant. Our models are in accelerating phase which is consistent to the recent observations. It has been found that the displacement vector β behaves like cosmological term Λ in the normal gauge treatment and the solutions are consistent with recent observations of SNe Ia. It has been found that massive strings dominate in the both decelerating and accelerating universes. The strings dominate in the early universe and eventually disappear from the universe for sufficiently large times. This is in consistent with the current observations. Some physical and geometric behaviour of these models are also discussed.     

A Plane-Symmetric Magnetized Inhomogeneous Cosmological Models of Perfect Fluid Distribution with Variable Magnetic Permeability in Lyra Geometry

A plane-symmetric magnetized inhomogeneous cosmological model of the universe with time dependent gauge function β for perfect fluid distribution with variable magnetic permeability within the framework of Lyra geometry is investigated. The source of the magnetic field is due to an electric current produced along the z-axis. Thus F ₁₂ is the only non-vanishing component of electromagnetic field tensor F _ij . To get a deterministic solution of Einstein’s modified field equations, the free gravitational field is assumed to be Petrov type-II non-degenerate. For our derived model we obtain the deceleration parameter q=−1 as in the case of de Sitter universe. It has been found that the displacement vector β(t) behaves like cosmological term Λ in the normal gauge treatment and the solution is consistent with the observations. The displacement vector β(t) affects entropy. Some physical and geometric properties of the model are also discussed.     

Some Exact Solutions of String Cosmological Models in?Bianchi Type-II Space-Time

The Bianchi type-II cosmological solutions of massive strings have been investigated in the presence as well as absence of the magnetic field. The energy conditions for a cloud of strings coupled to the Einstein equations have been examined. The physical features of the models have also been discussed.     

A Cosmological Model of the Early Universe Based on ECG with Variable Λ-Term in Lyra Geometry

In this paper, we study interacting extended Chaplygin gas as dark matter and quintessence scalar field as dark energy with an effective Λ-term in Lyra manifold. As we know Chaplygin gas behaves as dark matter at the early universe while cosmological constant at the late time. Modified field equations are given and motivation of the phenomenological models discussed in details. Four different models based on the interaction term are investigated in this work. Then, we consider other models where Extended Chaplygin gas and quintessence field play role of dark matter and dark energy respectively with two different forms of interaction between the extended Chaplygin gas and quintessence scalar field for both constant and varying Λ. Concerning to the mathematical hardness of the problems we discuss results numerically and graphically. Obtained results give us hope that proposed models can work as good models for the early universe with later stage of evolution containing accelerated expansion.     

Bulk Viscous Bianchi Type V Cosmological Models with Decaying Cosmological Term Λ

We present bulk viscous Bianchi type V cosmological models with time-dependent cosmological term Λ. Exact solutions of Einstein field equations have been obtained by assuming shear scalar σ proportional to volume expansion θ. The coefficient of bulk viscosity is taken to be power function of energy density ρ or volume expansion θ. In these models cosmological term Λ come out to be negative. It is found that models obtained are expanding, shearing and non-rotating. They do not approach isotropy for large values of time t. Some observational parameters for the model have also been discussed.     

Bulk Viscous Bianchi Type I Cosmological Models with Time-Dependent Cosmological Term Λ

Bianchi type I cosmological models with time-varying cosmological constant Λ and bulk viscous fluid are investigated. Cosmic matter is chosen to obey a barotropic equation of state. Exact solutions of Einstein’s field equations are obtained assuming the volume expansion θ proportional to the eigen values of shear tensor σ _ij . Physical and kinematical properties of the models are discussed considering bulk viscosity to be a power function of matter density.     

Bianchi Type-III Cosmological Models with Gravitational Constant G and the Cosmological Constant ∧

Einstein field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-Ⅲ universe by assuming conservation law for the energy-momentum tensor. Exact solutions of the field equations are obtained by using the scalar of expansion proportional to the shear scalar θ∝σ, which leads to a relation between metric potential B = Cn, where n is a constant. The corresponding physical interpretation of the cosmological solutions are also discussed.     

FRW Cosmological Models with Bulk-Viscosity in?Barber’s Second Self-Creation Theory

We have studied the evolution of spatially homogeneous and isotropic FRW cosmological model with bulk-viscosity in the frame work of Barber’s (Gen. Relativ. Gravit. 14: 117, 1982) second self-creation theory of gravitation. The cosmological models are obtained with the help of special law of variation for Hubble parameter proposed by Bermann (Nuovo Cimento 74B: 182, 1983). Physical parameters of the models have been discussed in case of false vacuum model, Zel’dovich fluid and radiation dominated fluid.     

Lyra’s Cosmology of Massive Strings in Anisotropic Bianchi-II Space-Time

The paper deals with a spatially homogeneous and totally anisotropic Bianchi II cosmological models representing massive strings in normal gauge for Lyra’s manifold. The modified Einstein’s field equations have been solved by applying variation law for Hubble’s parameter. This law generates two type of solutions for average scale factor, one is of power law type and other is of exponential law type. The power law describes the dynamics of Universe from big bang to present epoch while exponential law seems reasonable to project dynamics of future Universe. It has been found that the displacement vector (β) is a decreasing function of time and it approaches to small positive value at late time, which is collaborated with Halford (Aust. J. Phys. 23, 863, 1970) as well as recent observations of SN Ia. The study reveals that massive strings dominate in early Universe and eventually disappear from Universe for sufficiently large time, which is in agreement with the current astronomical observations.     

Bianchi Type-Ⅲ String Cosmological Models with Time Dependent Bulk Viscosity

Bianchi type-Ⅲ string cosmological models with bulk viscous fluid for massive string are investigated. To obtain the determinate model of the universe, we assume that the coeffcient of bulk viscosity ξ is inversely proportional to the expansion θ in the model and expansion θ in the model is proportional to the shear g. This leads to B =lC^n, where l and n are constants. Behaviour of the model in the presence and absence of bulk viscosity is discussed. The physical implications of the models are also discussed in detail.     

Isotropization of Bianchi Models and a New FRW Solution in Brans–Dicke Theory

Using scaled variables we are able to integrate an equation valid for isotropic and anisotropic Bianchi type I, V, IX models in Brans–Dicke (BD) theory. We analyze known and new solutions for these models in relation with the possibility that anisotropic models asymptotically isotropize, and/or possess inflationary properties. In particular, a new solution of curved (k 0) Friedmann–Robertson–Walker (FRW) cosmologies in Brans–Dicke theory is analyzed.     

Anisotropic Bianchi Type Ⅰ Cosmological Models with Generalized Chaplygin Gas and Dynamical Gravitational and Cosmological Constants

This paper deals with study of generalized Chaplygin gas model with dynamical gravitational and cosmological constants. In this paper a new set of exact solutions of Einstein field equations for spatially homogeneous and anisotropic Bianchi type Ⅰ space-time have been obtained. The solutions of the Einstein's field equations are obtained by considering(i) the power law relation between Hubble parameter H and scale factor R and(ii) scale factor of the form R =-1/t + t~2, t 1. The assumptions lead to constant and variable deceleration parameter respectively. The physical and dynamical behaviors of the models have been discussed with the help of graphical representations. Also we have discussed the stability and physical acceptability of solutions for solution type-Ⅰ and solution type-Ⅱ.     

Bianchi Type-Ⅱ Inflationary Models with Stiff Matter and Decaying Cosmological Term

We deal with Einstein＇s field equations with a time-decaying cosmological term of the forms （i） ∧=β（a/a） ＋ α/a62 and （ii）∧ = α/a^2, where a is the average scale factor of the universe, α and β are constants for a spatially homogeneous and anisotropic LRS Bianchi type-Ⅱ spacetime. Exact solutions of the field equations for stiff matter are obtained by applying a special law of variation for the Hubble parameter. Anisotropic cosmological models are presented with a constant negative deceleration parameter which corresponds to the accelerated phase of the present universe. The cosmological constant A is obtained as a decreasing function of time that is approaching a small positive value at the present epoch, which is corroborated by the consequences from recent supernovae Ia observations. The physical and kinematical behaviors of the models are also discussed.     

A Class of New Nonlinear Bogoliubov Transformations

We find a class of new nonlinear Bogolubov transformations and solve the eigenvalue problem of the model Hamiltonian describing the second harmonic generation with intensity-dependent coupling.These transformations differ from the previously known nonlinear quadrature-dependent bogoliubov transformations.     

On Measuring Standards in Weyl’s Geometry

In Weyl’s geometry the nonintegrability problem and difficulties in defining measuring standards are reconsidered. Approaches removing the nonintegrability of length in the interior of atoms are given, so that atoms can serve as measuring standards. The Weyl space becomes a well founded framework for classical theories of electromagnetism and gravitation.