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.     

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.     

Higher Dimensional Cosmological Model With Gravitational and Cosmological "Constants"

In this paper we have considered a cosmological model representing a flat viscous universe with variable G and in the context of higher dimensional spacetime. It has been observed that in this model the particle horizon exists and the cosmological term varies as inverse square of time. The deceleration parameter and temperature are well within the observational limits. The model indicates matter and entropy generation in the early stages of the universe. Further, it is shown that our model generates all models obtained by Arbab and Singh et al. in four-dimensional space-time.     

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.     

Interacting Viscous Modified Chaplygin Gas Cosmology in Presence of Cosmological Constant

Here, we consider interacting viscous modified Chaplygin gas in presence of cosmological constant. We assumed bulk viscosity as a function of density. We consider interaction between modified Chaplygin gas and baryonic matter. Then, the effects of viscosities on the cosmological parameters such as energy, density, Hubble expansion parameter, scale factor and deceleration parameter investigated. This model may be considered as a toy model of our universe.     

Cosmological Models with Linearly Varying Deceleration Parameter

We propose a new law for the deceleration parameter that varies linearly with time and covers Berman’s law where it is constant. Our law not only allows one to generalize many exact solutions that were obtained assuming constant deceleration parameter, but also gives a better fit with data (from SNIa, BAO and CMB), particularly concerning the late time behavior of the universe. According to our law only the spatially closed and flat universes are allowed; in both cases the cosmological fluid we obtain exhibits quintom like behavior and the universe ends with a big-rip. This is a result consistent with recent cosmological observations.     

Generalized Chaplygin Gas Dominated Anisotropic Bianchi Type-I Cosmological Models

We present Bianchi type-I cosmological models in the presence of generalized Chaplygin gas and perfect fluid for early and late time epochs. Exact solutions of Einstein’s field equations for this model are obtained. The general solutions of gravitational field equations are expressed in an exact parametric form, with average scale factor as parameter. In the limiting cases of small and large values of the average scale factor, the solutions of the field equations are expressed in exact analytic forms. Moreover, this model predicts that the expansion of Universe is accelerating for the late times. The physical and geometrical properties of the corresponding cosmological models are discussed.     

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.     

Cosmological model with viscosity media (dark fluid) described by an effective equation of state

A generally parameterized equation of state (EOS) is investigated in the cosmological evolution with bulk viscosity media modelled as dark fluid, which can be regarded as a unification of dark energy and dark matter. Compared with the case of the perfect fluid, this EOS has possessed four additional parameters, which can be interpreted as the case of the non-perfect fluid with time-dependent viscosity or the model with variable cosmological constant. From this general EOS, a completely integrable dynamical equation to the scale factor is obtained with its solution explicitly given out. (i) In this parameterized model of cosmology, for a special choice of the parameters we can explain the late-time accelerating expansion universe in a new view. The early inflation, the median (relatively late time) deceleration, and the recently cosmic acceleration may be unified in a single equation. (ii) A generalized relation of the Hubble parameter scaling with the redshift is obtained for some cosmology interests. (iii) By using the SNe Ia data to fit the effective viscosity model we show that the case of matter described by p=0$p=0$ plus with effective viscosity contributions can fit the observational gold data in an acceptable level.     

Cosmological models with constant deceleration parameter and bulk viscous mode

Recently Berman and Gomide have presented cosmological models with a constant deceleration parameter in general relativity without assuming a specific equation of state. It is shown that these models are equivalent to those with bulk viscosity. Some general remarks are made on the former models, including implications for violations of causality.     

Bulk Viscous Bianchi Type-V Cosmological Models with Variable Gravitational and Cosmological Constant

This paper deals with Bianchi type-V cosmological models of the universe filled with a bulk viscous cosmic fluid in the framework of general relativity. A new class of exact solutions has been obtained by considering various well established power law relations among scale factor, cosmological and gravitational constants and cosmic time. Some physical and geometrical behaviors of the models have also been discussed. It has been found that all the models are in fair agreement of observational results.     

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.     

The $$B\rightarrow \bar{K}\pi \ell \ell $$ distribution at low hadronic recoil

The general class of Bianchi cosmological models with dark energy in the form of modified Chaplygin gas with variable Λ and G and bulk viscosity have been considered. We discuss three types of average scale factor by using a special law for deceleration parameter which is linear in time with negative slope. The exact solutions to the corresponding field equations are obtained. We obtain the solution of bulk viscosity (ξ), cosmological constant (Λ), gravitational parameter (G) and deceleration parameter (q) for different equations of state. The model describes an accelerating Universe for large value of time t, wherein the effective negative pressure induced by Chaplygin gas and bulk viscous pressure are driving the acceleration.     

Locally-rotationally-symmetric Bianchi type-V cosmology with heat flow

In this paper we present a spatially homogeneous locally-rotationally-symmetric (LRS) Bianchi type-V cosmological model with perfect fluid and heat flow. A general approach is introduced to solve Einstein’s field equations using a law of variation for the mean Hubble parameter, which is related to average scale factor of the model that yields a constant value for the deceleration parameter. Exact solutions that correspond to singular and non-singular models are found with heat flow. The physical constraints on the solution and, in particular, the thermodynamical laws that govern such solutions are discussed in some detail.     

Bulk viscous cosmology in early Universe

The effect of bulk viscosity on the early evolution of Universe for a spatially homogeneous and isotropic Robertson-Walker model is considered. Einstein’s field equations are solved by using ‘gamma-law’ equation of state p = (γ − 1)ρ, where the adiabatic parameter gamma (γ) depends on the scale factor of the model. The ‘gamma’ function is defined in such a way that it describes a unified solution of early evolution of the Universe for inflationary and radiation-dominated phases. The fluid has only bulk viscous term and the coefficient of bulk viscosity is taken to be proportional to some power function of the energy density. The complete general solutions have been given through three cases. For flat space, power-law as well as exponential solutions are found. The problem of how the introduction of viscosity affects the appearance of singularity, is briefly discussed in particular solutions. The deceleration parameter has a freedom to vary with the scale factor of the model, which describes the accelerating expansion of the Universe.      

Cosmological shock waves in general relativity

The problem of finding spherically symmetric self-similar solutions of Einstein's field equations with a barotropic perfect fluid, which can be joined through a shock wave to some cosmological models, is considered. It is found that such solutions comprise an expanding shell of matter surrounding a horizon with an interior singularity.     

FRW Cosmology and Static Extra Dimension with Non-zero Cosmological Constant

In this paper we consider a five dimensional FRW cosmology with static extra dimension and obtain field equations including cosmological constant. We solve field equations and obtain the scale factor, energy density, pressures, and deceleration parameter. The constant coefficients play very important rule in our results, so that they obtained by comparing with observational data.     

Warm-Polytropic Cosmology with and Without Bulk Viscosity

In this paper we consider warm-polytropic cosmology including bulk viscosity and study cosmological parameters. We can obtain effect of viscosity on the important cosmological parameters such as Hubble expansion, deceleration and scale factor parameters. We compare our results with observational data and fix our solution. We find that the bulk viscosity increases both energy density and Hubble expansion parameter.     

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.     

An inhomogeneous model universe behaving homogeneously

We present a new model universe based on the junction of FRW to flat Lemaitre–Tolman–Bondi (LTB) solutions of Einstein equations along our past light cone, bringing structures within the FRW models. The model is assumed globally to be homogeneous, i.e. the cosmological principle is valid. Local inhomogeneities within the past light cone are modeled as a flat LTB, whereas those outside the light cone are assumed to be smoothed out and represented by a FRW model. The model is singularity free, always FRW far from the observer along the past light cone, gives way to a different luminosity distance relation as for the CDM/FRW models, a negative deceleration parameter near the observer, and correct linear and non-linear density contrast. As a whole, the model behaves like a FRW model on the past light cone with a special behavior of the scale factor, Hubble and deceleration parameter, mimicking dark energy. Paper in honor of Bahram Mashhoon’s 60th birthday.