Anisotropic Dark Energy Bianchi Type-II Cosmological Models in Lyra Geometry

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological model has been discussed in general relativity in the presence of a hypothetical anisotropic dark energy fluid with constant deceleration parameter within the frame work of Lyra’s manifold with uniform and time varying displacement field vector. With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983) a dark energy cosmological model is obtained in this theory. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.     

Some Exact Bianchi Type-V Perfect Fluid Cosmological Models with Heat Flow and Decaying Vacuum Energy Density Λ: Expressions for Some Observable Quantities

In this paper we have obtained some new exact solutions of Einstein’s field equations in a spatially homogeneous and anisotropic Bianchi type-V space-time with perfect fluid distribution along with heat-conduction and decaying vacuum energy density Λ by applying the variation law for generalized Hubble’s parameter that yields a constant value of deceleration parameter. We find that the constant value of deceleration parameter is reasonable for the present day universe. 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 form. Using these two forms, Einstein’s field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The cosmological constant Λ is found to be a decreasing function of time and positive which is corroborated by results from recent supernovae Ia observations. Expressions for look-back time-redshift, neoclassical tests (proper distance d(z)), luminosity distance red-shift and event horizon are derived and their significance are described in detail. The physical and geometric properties of spatially homogeneous and anisotropic cosmological models are discussed.     

Bianchi V Cosmology with a Specific Hubble?Parameter

In the present paper, we investigate the possibility of a variation law for Hubble’s parameter H in the background of spatially homogeneous, anisotropic Bianchi type V space-time with perfect fluid source and time-dependent cosmological term. The model obtained presents a cosmological scenario which describes an early deceleration and late time acceleration. The model approaches isotropy and tends to a de Sitter universe at late times. The cosmological term Λ asymptotically tends to a genuine cosmological constant. It is observed that the solution is consistent with the results of recent observations.     

Bianchi-I Space-time with Variable Gravitational and?Cosmological “Constants”

We consider Einstein’s field equations with variable gravitational and cosmological “constants” for a spatially homogeneous and anisotropic Bianchi-I space-time. A law of variation for the Hubble parameter, which is related to the average scale factor and yields a constant value of the deceleration parameter, is assumed to solve the field equations. The gravitational constant is allowed to follow a power-law form. We find that a time-increasing gravitational constant is suitable for describing the present evolution of universe. The solutions reveal the dynamics of a universe, which expands forever. The physical interpretation of the solutions is discussed in detail.     

Viscous Cosmological Model with Variable Gravitational and Cosmological Constants

We have considered some cosmological solutions with variable gravitational and cosmological constants with bulk viscosity. It is found that the solutions are singularity free and the deceleration parameter is in general not a constant unless we assume perfect fluid with equation of state in the standard cosmologies. Moreover, the deceleration parameter is a function of the scale factor and changes sign with evolution, so our solution is a generalization of those obtained by Arbab I. Arbab. The introduction of viscosity not only free from singularity but also give the deceleration parameter a freedom to vary with scale factor. Thus, a viscous cosmological fluid gives a more general situation in the early universe.     

Some Exact Bianchi Type V Perfect Fluid Solutions with Heat Flow

The variation law for generalized mean Hubble’s parameter is discussed in a spatially homogeneous and anisotropic Bianchi type V space-time with perfect fluid along with heat-conduction. The variation law for Hubble’s parameter, that yields a constant value of deceleration parameter, generates two types of solutions for the average scale factor, one is of power-law type and other one of exponential form. Using these two forms of the average scale factor, exact solutions of Einstein field equations with a perfect fluid and heat conduction are presented for a Bianchi type V space-time, which represent expanding singular and non-singular cosmological models. We find that the constant value of deceleration parameter is reasonable for the present day universe. The physical and geometrical properties of the models are also discussed in detail.     

Viscous Fluid Cosmology in Bianchi Type-I Space-Time

The paper presents a spatially homogeneous and anisotropic Bianchi type-I cosmological model consisting of a dissipative fluid. The field equations are solved explicitly by using a law of variation for mean Hubble parameter, which is related to average scale factor and yields a constant value for deceleration parameter. We find that the constant value of deceleration parameter describes the different phases of the evolution of universe. A barotropic equation of state (p=γ ρ) together with a linear relation between shear viscosity and expansion scalar, is assumed. It is found that the viscosity plays a key role in the process of the isotropization of the universe. The presence of viscous term does not change the fundamental nature of initial singularity. The thermodynamical properties of the solutions are studied and the entropy distribution is also given explicitly.     

The dynamical evolution of 3-space in a higher dimensional steady state universe

We investigate a class of cosmological solutions of Einstein’s field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject to two constraints that (i) the total volume scale factor of the universe is constant and (ii) the effective energy density is constant. We obtain various interesting new dynamics for the external space that yield a time varying deceleration parameter including oscillating cases when the flat/curved external and curved/flat internal spaces are considered. We also comment on how the universe would be conceived by an observer in four dimensions who is unaware of the extra dimensions.     

A Cosmological Model with Negative Constant Deceleration Parameter in Brans-Dicke Theory

Bermann (1983) [Nuovo Cimento B, 74, 182] obtained a cosmological model with the help of special law of variation for Hubble's parameter that yields constant deceleration parameter models of the universe. Here, we present Bianchi-I model with negative constant deceleration parameter in Brans-Dicke (1961) [Phys. Rev., 124, 925] theory in the presence of perfect fluid source with disordered radiation. Some physical properties of the model are also discussed. PACS numbers: 98-90.     

Anisotropic Bianchi Type-II Massive String Cosmological Models with Time-Decaying Λ Term and Thermodynamic Parameters

The present paper envisages a spatially homogeneous and anisotropic Bianchi II massive string cosmological models with time-decaying Λ term in general relativity. By using the variation law of Hubble’s parameter, the Einstein’s field equations have been solved for two general cases. The first case involving a power law solution describes the dynamics of universe from big bang to present epoch while the second case admit an exponential solution seems reasonable to project dynamics of future universe. We observed that massive strings dominate in early universe and eventually disappear at late time, which is consistent with the current astronomical observations. It has been found that the cosmological constant (Λ) is a decreasing function of time and it approaches to small positive value at sufficiently large time. The thermodynamic properties of anisotropic Bianchi II universe are studied and also the absolute temperature and entropy distribution are given explicitly. The relations between thermodynamic parameters and cosmological constant Λ has been established. Physical behavior of the derived model is elaborated in detail.     

LRS Bianchi Type-I Dark Energy Cosmological Model in Brans-Dicke Theory of Gravitation

Bianchi type-I dark energy model with variable equation of state (EoS) parameter is presented in a scalar-tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961). To get a determinate solution of the field equations we will take the help of special law of variation for Hubble’s parameter presented by Bermann (Nuovo Cimento B. 74:182, 1983) which yields a dark energy cosmological model with negative constant deceleration parameter. It is observed that this dark energy cosmological model always represents an accelerated and expanding universe and also consistent with the recent observations of type-Ia supernovae. Some physical and geometrical properties of the model are also discussed.     

Statefinders and observational measurement of superenergy

The superenergy of the universe is a tensorial quantity and it is a general relativistic analogue of the Appell's energy of acceleration in classical mechanics. We propose the way to measure this quantity by the application of the observational parameters such as the Hubble parameter, the deceleration parameter, the jerk and the snap (kerk), known as statefinders. We show that the superenergy of gravity requires only the Hubble and deceleration parameters to be measured, while the superenergy of matter requires also the measurement of the higher-order characteristics of expansion: the jerk and the snap. In such a way, the superenergy becomes another parameter characterizing the evolution of the universe. One of the interesting points is that the cosmological constant has a purely gravitational interpretation in terms of superenergy.     

A new class of cosmological models in Lyra geometry

FRW 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. Dedicated to Professor V B Johri on his sixtieth birthday.     

Two-Fluid Cosmological Model of Bianchi Type-V with Negative Constant Deceleration Parameter

This paper deals with a two-fluid Bianchi type-V anisotropic cosmological model with negative constant deceleration parameter. Exact solution of Einstein’s field equations for interacting matter and radiation field is presented which represents an expanding shearing and nonrotating cosmological model of the universe. This model describes the accelerated phase of the expanding universe. The physical and kinematical behaviors of the model are discussed.     

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.     

Magnetized String Cosmology in Anisotropic Bianchi-II Space-time with Variable Cosmological Term-Λ

The present study deals with a spatially homogeneous and anisotropic Bianchi-II cosmological models representing massive strings by applying the variation law for generalized Hubble’s parameter that yields a constant value of deceleration parameter. We find that the constant value of deceleration parameter is reasonable for the present day universe. 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 form. Using these two forms, Einstein’s 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 (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 s¹₁\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. The cosmological constant Λ is found to be a decreasing function of time and it approaches a small positive value at present epoch which is in good agreement by the results from recent supernovae observations. Some physical and geometric behaviour of the models are also discussed.     

Bianchi Type-I Space-Time with Variable Cosmological Constant

A spatially homogeneous and anisotropic Bianchi type-I perfect fluid model is considered with variable cosmological constant. Einstein’s field equations are solved by using a law of variation for mean Hubble’s parameter, which is related to average scale factor and that yields a constant value of deceleration parameter. An exact and singular Bianchi-I model is presented, where the cosmological constant remains positive and decreases with the cosmic time. 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 model is carried out.     

The solution of the cosmological constant problem from the inhomogeneous equation of state — a hint from modified gravity?

The cosmological constant problem is studied in a two component cosmological model. The universe contains a cosmological constant of an arbitrary size and sign and an additional component with an inhomogeneous equation of state. It is shown that, in a proper parameter regime, the expansion of the universe with a large absolute value of the cosmological constant may asymptotically tend to de Sitter space corresponding to a small effective positive cosmological constant. It is argued that such a behavior can be regarded as a solution of the cosmological constant problem in this model. The mechanism behind the relaxation of the cosmological constant is discussed. A connection with modified gravity theories is discussed and an example of a possible realization of the cosmological constant relaxation in f(R) modified gravity is described.     

Time evolution of the cosmological “constant”

We discuss cosmologies where the cosmological constant λ depends on time. The requirements of realistic cosmology impose restrictions on the functional dependence of λ on the Hubble parameter H. We show that for a wide class of functions with λ of the order H³ the system of field equations leads to a stable fix-point behaviour with λ naturally very small today. The age of the universe, critical matter density and deceleration parameter may be modified.     

Two Fluids Tilted Cosmological Models in General Relativity

Tilted homogeneous plane symmetric two fluids cosmological models with matter and radiating source are investigated. In the model one of the fluids represents the matter content of the universe and another fluid is the CMB radiation. The tiltedness is also considered .With the help of variation for Hubble’s parameter proposed by Bermann a cosmological model with negative constant deceleration parameter is obtained. We have also investigated the behaviours of some physical parameters.