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.     

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.     

Bianchi types I and V bulk viscous fluid cosmological models in f(R,T) gravity theory

In this paper we present non-singular Bianchi types I and V cosmological models, in the presence of bulk viscous fluid and within the framework of f(R,T) gravity theory. Exact solutions to the field equations are obtained by choosing a particular form of the function f(R,T) and a special value for the average scale factor of the model, which corresponds to a time- dependent deceleration parameter. The cosmological models initially accelerate for a certain period of time and thereafter decelerate. The physical and kinematical properties of the models of the universe are discussed.     

Anisotropic Bianchi type V perfect fluid cosmological models in Lyra’s geometry

The law of variation for mean Hubble’s parameter with average scale factor, in an anisotropic Bianchi type V cosmological space–time, is discussed within the frame work of Lyra’s manifold. The variation of Hubble’s parameter, which gives a constant value of deceleration parameter, generates two types of solutions for the average scale factor; one is the power-law and the other one is of exponential form. Using these two forms, new classes of exact solutions of the field equations have been found for a Bianchi type V space–time filled with perfect fluid in Lyra’s geometry by considering a time-dependent displacement field. The physical and kinematical behaviors of the singular and non-singular models of the universe are examined. Exact expressions for look-back time, luminosity distance and event horizon versus redshift are also derived and their significance are discussed in detail. It has been observed that the solutions are compatible with the results of recent observations.     

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.     

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.     

Nonstatic Gödel-type cosmological model with perfect fluid and heat flow

We obtain some cosmological models that are exact solutions of Einstein field equations. The metric utilized is the nonstatic Gödel-type cosmological model and the curvature source is a perfect fluid with heat flow. The solutions reported here are nonstatic generalizations of Gödel's rotating cosmos.     

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.     

Ab-initio calculations of electric field gradient in Ru compounds and their implication on the nuclear quadrupole moments of $$^{99}\hbox {Ru}$$ and $$^{101}\hbox {Ru}$$101Ru

We study a spatially homogeneous and anisotropic cosmological model in the Einstein gravitational theory with a minimally coupled scalar field. We consider a non-interacting combination of scalar field and perfect fluid as the source of matter components which are separately conserved. The dynamics of cosmic scalar fields with a zero rest mass and an exponential potential are studied, respectively. We find that both assumptions of potential along with the average scale factor as an exponential function of scalar field lead to the logarithmic form of scalar field in each case which further gives power-law form of the average scale factor. Using these forms of the average scale factor, exact solutions of the field equations are obtained to the metric functions which represent a power-law and a hybrid expansion, respectively. We find that the zero-rest-mass model expands with decelerated rate and behaves like a stiff matter. In the case of exponential potential function, the model decelerates, accelerates or shows the transition depending on the parameters. The isotropization is observed at late-time evolution of the Universe in the exponential potential model.     

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.      

New classes of exact solutions in inflationary cosmology

The problem of determining a representation of the self-interaction potential in the form of a time dependence of the field potential energy which admits the existence of an inflationary regime and the transition of evolution to a Friedmann regime of asymptotic expansion is investigated within a cosmological model with a self-interacting scalar field. A variational formulation of the slow-roll concept is introduced, and, on the basis thereof, an exact solution is constructed for the evolution of the scale factor and the form of the self-interaction potential. A method based on representing the Einstein equations in the form of a linear second-order equation is developed for constructing and analyzing exact cosmological solutions of these equations. Selected types of potentials and the corresponding evolutions of the universe are investigated. Zh. éksp. Teor. Fiz. 114, 406–417 (August 1998)     

FRW-Cosmological Model for Conharmonically Flat Space Time

This paper deals with FRW-Cosmological model of the universe for conharmonically flat space time. Einstein field equations with variable cosmological term are solved by using a law of variation for Hubble’s parameter, which is related to average scale factor. A new class of exact solution of the field equation has been obtained in which cosmological-term decreases with cosmic time. A detailed study of physical and kinematical properties of the model is also carried out.     

Quintessential Inflation with Dissipative Fluid

We have investigated cosmological models with a self-interacting scalar field and a dissipative matter fluid as the sources of matter. Different variables are expressed in terms of a generating function. Exact solutions are obtained for one particular choice of the generating function. The potential corresponding to this generating function is a standard tree-level potential arising in the perturbative regime in quantum field theory. With suitable choice of parameters, the scale factor in our model exhibits both decelerating behaviour in the early time as well as an accelerating phase at late times. For certain choices of the parameter the solution also exhibits an attractor nature towards an asymptotic de-Sitter universe.     

Early Universe with Variable Cosmological Constants in Higher Dimensional Space Time

The field equations with variable cosmological and gravitational constants are consider in the presence of perfect fluid for Kaluza-Klein type cosmological model. The exact solutions of the field equations are obtained by using the gamma law equation of state p=(γ−1)ρ in which the parameter γ depends on scale factor R. The functional form of γ(R) is used to analyze a wide range of cosmological solution at early universe for two phases in cosmic history: inflationary phase and radiation dominated phase. The corresponding physical interpretation of cosmological solution are also discussed in the framework of higher dimensional space time.     

On quintessential cosmological models and exponential potentials

We first study dark energy models with a minimally-coupled scalar field and generalized exponential potentials, admitting exact solutions for the cosmological equations: actually, it turns out that for this class of potentials the Einstein field equations exhibit alternative Lagrangians, and are completely integrable and separable. We analyze their analytical solutions, especially discussing when they are compatible with a late time quintessential expansion of the universe. As a further issue, we discuss how quintessential scalar fields with exponential potentials can be connected to the inflationary phase, building up a quintessential inflationary scenario: actually, it turns out that the transition from inflation toward late-time exponential quintessential tail admits a kination period, which is an indispensable ingredient of this kind of theoretical models. All such considerations have been made by including also radiation into the model.     

Anisotropic Cosmological Models with Quintessence

In this paper anisotropic cosmological models with bulk viscosity and quintessence have been studied. Some exact solutions of Einstein field equations with bulk viscosity and quintessence on the background of anisotropic Bianchi Type I space-time are obtained. The new cosmological models approach to isotropy with evolution of the universe. Physical properties of these cosmological models have also been discussed.     

Anisotropic Bulk Viscous Fluid Cosmological Model with Zero-Rest-Mass Scalar Field and Time-Dependent Cosmological Term

In this paper, we have investigated Bianchi type-III cosmological model in the presence of a bulk viscous fluid together with zero-rest-mass scalar field and time-dependent cosmological term. We have shown that the field equations are solvable for any arbitrary cosmic scale function. Exact solutions of Einstein’s field equations are obtained which represent an expanding, shearing, non-rotating and decelerating model of the universe. Some physical and geometrical behaviours of the cosmological model are discussed.     

Cosmological Models with Time Dependent G and Λ Coupling Scalars

A cosmological model in which the universe has its critical density and gravitational constants generalized as coupling scalars in Einstein's theory is considered. A general method of solving the field equations is given. An exact solution for matter distribution in cosmological models satisfying G=G₀(R/R₀)ⁿ is presented. Corresponding physical interpretations of the cosmological solutions are also discussed.