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 Bulk Viscous Barotropic Fluid Cosmological Models with Variable G and Λ

Bianchi type-Ⅲ bulk viscous barotropic fluid cosmological model with variables G and A is investigated. To obtain the realistic model, we assume the conditions between the metric potentials A, B, C as A/A = B/B = m1/t^N and C/C = m2/t^n, P = p - 3ηH, η =ηop^s, p=γρ, 0 ≤ γ ≤ 1, where p is isotropic pressure,η the coefficient of bulk viscosity, η0 and S the constants, H the Hubble constant, m1 = 2m2 where m1 〉 0, m2 〉 O. The solutions obtained lead to inflationary phase and the results obtained match with the observations. The case n = 1 for S = 1 is also discussed, relating the results with the observations.     

Bulk Viscous Cosmological Models with Variable G and Λ

Einstein's equations with variable gravitational and cosmological constants are considered in the presence of bulk viscosity for the spatially flat homogeneous and isotropic universe in a way which conserves the energy momentum tensor. A solution is found in which the cosmological term varies inversely with the square of time. Our approach is compared with that of Arbab.     

LRS Bianchi Type II Bulk Viscous Fluid Universe with?Decaying Vacuum Energy Density Λ

The present study deals with spatially homogeneous and locally rotationally symmetric (LRS) Bianchi type II cosmological models with bulk viscous fluid distribution of matter and decaying vacuum energy density Λ. 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. The vacuum energy density Λ for both models is found to be a decreasing function of time and it approaches a small positive value at late time which is supported by recent results from the observations of (SN Ia). Some physical and geometric behaviour of these models are also discussed.     

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.     

Bianchi Type-V Bulk Viscous Barotropic Fluid Cosmological Model with Variable G and Λ

We investigate the Bianchi type-V bulk viscous barotropic fluid cosmological model with variable gravitational constant G and the cosmological constant A, assuming the condition on metric A/A=B/B=C/C=m/tn potential aswhere A, B, and C are functions of time t, while m and n are constants. To obtain the deterministic mo del, we also assume the relations P = p - 3η H, p = 7P, η = ηop^s, where p is the isotropic pressure, η the bulk viscosity,0≤r≤1 H the Hubble constant, ηo and s are constants. Various physical aspects of the model are discussed.The case of n = 1 is also discussed to compare the results with the actual universe.     

Bianchi Type Ⅲ String Cosmological Model with Bulk Viscosity

The Bianchi type Ⅲ cosmological model for a cloud string with bulk viscosity are presented. To obtaina determinate model, an equation of state p = κλ and a relation between metric potentials B = Cn are assumed. Thephysical and geometric aspects of the model are also discussed. The model describes a shearing non-rotating continuouslyexpanding universe with a big-bang start, and the relation between the coefficient of bulk viscosity and the energy densityis ζ∝1 p1/2.     

Bianchi Type Ⅲ String Cosmological Model with Bulk Viscosity

The Bianchi type Ⅲ cosmological model for a cloud string with bulk viscosity are presented. To obtain a determinate model, an equation of state ρ=kλ and a relation between metric potentials B = C^n are assumed. The physical and geometric aspects of the model are also discussed. The model describes a shearing non-rotating continuously expanding universe with a big-bang start, and the relation between the coefficient of bulk viscosity and the energy density is ζ∝ρ^1/2.     

Kaluza-Klein Type Robertson Walker Cosmological Model with Dynamical Cosmological Term Λ

In this paper we have analyzed the Kaluza-Klein type Robertson Walker (RW) cosmological models by considering three different forms of variable Λ: , and Λ∼ρ. It is found that, the connecting free parameters of the models with cosmic matter and vacuum energy density parameters are equivalent, in the context of higher dimensional space time. The expression for the look back time, luminosity distance and angular diameter distance are also derived. This work has thus generalized to higher dimensions the well-known results in four dimensional space time. It is found that there may be significant difference in principle at least, from the analogous situation in four dimensional space time.     

Bianchi Type I Viscous Universe with Variable G and Λ

Exact solutions for an anisotropic Bianchi type I model with bulk viscosity and variable G and are obtained. We have found some solutions that correspond to our earlier work for the isotropic one. Unlike Kalligas et al., an inflationary solution with a variable energy density has been found where the anisotropy energy decreases exponentially with time. There is a period of hyper-inflation during which the energy density remains constant.     

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.     

Causal Viscous Cosmological Models With Variable G and Λ

Einstein's equations with variable gravitational and cosmological constants are considered in the presence of a bulk viscous fluid source described by the truncated causal theory of Israel–Stewart, for the spatially flat homogeneous and isotropic universe. A solution is found in which the cosmological term varies inversely with the square of time. However, the gravitational constant G is found to be increasing with time.     

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.     

Magnetized Bianchi Type III String Universe with Time Decaying Vacuum Energy Density Λ

Exact solution of Einstein’s field equations is obtained for massive string cosmological model of Bianchi III space-time using the technique given by Letelier (Phys. Rev. D 28:2414, 1983) in presence of perfect fluid and decaying vacuum energy density Λ. To get the deterministic solution of the field equations the expansion θ in the model is considered as proportional to the eigen value s² ₂\sigma^{2}_{~2} of the shear tensor s^j _i\sigma^{j}_{~i} and also the fluid obeys the barotropic equation of state. It is observed that the particle density and the tension density of the string are comparable at the two ends and they fall off asymptotically at similar rate. But in early stage as well as at the late time of the evolution of the universe we have two types of scenario (i) universe is dominated by massive strings and (ii) universe is dominated by strings depending on the nature of the two constants L and ℓ. The value of cosmological constant Λ for the model is found to be small and positive which is supported by the results from recent supernovae Ia observations. Some physical and geometric properties of the model are also discussed.     

Bulk Viscous Bianchi Type-III Cosmological Model with Time-Dependent <Emphasis Type="Italic">G</Emphasis> and Λ

This paper deals with Bianchi type-III anisotropic cosmological model of the universe filled with a bulk viscous fluid with time varying gravitational and cosmological constants. It is 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 universe. The physical behaviour of the model has also been discussed.     

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.     

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.