Abstract:
We investigate the stability of the Einstein static universe as a non-LRS Bianchi type IX solution of the Einstein equations in the presence of both non-tilted and tilted fluids. We find that the static universe is unstable to homogeneous perturbations of Bianchi type IX to the future and the past.

Abstract:
The Locally Rotationally Symmetric (LRS) Bianchi type I cosmological model with variable modified Chaplygin gas having the equation of state =？/, where 0≤≤1, is a positive constant, and is a positive function of the average-scale factor () of the universe (i.e., =()) has been studied. It is shown that the equation of state of the variable modified Chaplygin gas interpolates from radiation-dominated era to quintessence-dominated era. The statefinder diagnostic pair (i.e., {,} parameter) is adopted to characterize different phases of the universe.

Abstract:
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 variable deceleration parameter models of the universe. We have compared our models with those of Einstein's field theory with the cosmological term $\Lambda$. Our frame of reference is restricted to the recent Ia observations of supernovae. Some physical behaviour of the models is also examined in the presence of perfect fluids.

Abstract:
The exact solutions of the Einstein field equations for dark energy (DE) in Locally Rotationally Symmetric (LRS) Bianchi type-I metric under the assumption on the anisotropy of the fluid are obtained for exponential volumetric expansion within the frame work of Lyra manifold for uniform and time varying displacement field. The isotropy of the fluid and space is examined.

Abstract:
An LRS Bianchi type-V cosmological models representing a viscous fluid distribution with a time dependent cosmological term $\Lambda$ is investigated. To get a determinate solution, the viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density. It turns out that the cosmological term $\Lambda(t)$ is a decreasing function of time, which is consistent with recent observations of type Ia supernovae. Various physical and kinematic features of these models have also been explored.

Abstract:
Locally rotationally symmetric (LRS) Bianchi Type I cosmological models are examined in the presence of dynamically anisotropic dark energy and perfect fluid. We assume that the dark energy (DE) is minimally interacting, has dynamical energy density, anisotropic equation of state parameter (EoS). The conservation of the energy-momentum tensor of the DE is assumed to consist of two separately additive conserved parts. A special law is assumed for the deviation from isotropic EoS, which is consistent with the assumption on the conservation of the energy-momentum tensor of the DE. Exact solutions of Einstein's field equations are obtained by assuming a special law of variation for the mean Hubble parameter, which yields a constant value of the deceleration parameter. Geometrical and kinematic properties of the models and the behaviour of the anisotropy of the dark energy has been carried out. The models give dynamically anisotropic expansion history for the universe that allows to fine tune the isotropization of the Bianchi metric, hence the CMB anisotropy.

Abstract:
A model of a cloud formed by massive strings is used as a source of LRS Bianchi type II with time decaying vacuum energy density $\Lambda$. To construct string cosmological models we have used the energy-momentum tensor for such string as formulated by Letelier (1983). The high nonlinear field equations have been solved for two types of strings, (i) Massive string and (ii) Nambu string. The expansion $\theta$ in the model is assumed to be proportional to the shear $\sigma$. This condition leads to $A=\beta B^{m}$, where $A$ and $B$ are the metric coefficients, $m$ is a constant and $\beta$ is an integrating constant. Our models are in accelerating phase which is consistent to the recent observations of supernovae type Ia. The physical and geometrical behavior of these models are also discussed.

Abstract:
A solution to the coincidence and Big Rip problems on the bases of an anisotropic space-time is proposed. To do so, we study the interaction between viscous dark energy and dark matter in the scope of the Bianchi type-I Universe. We parameterize the viscosity and the interaction between the two fluids by constants $\zeta_{0}$ and $\sigma$ respectively. A detailed investigation on the cosmological implications of this parametrization has been made. We have also performed a geometrical diagnostic by using the statefinder pairs $\{s, r\}$ and $\{q, r\}$ in order to differentiate between different dark energy models. Moreover, we fit the coupling parameter $\sigma$ as well as the Hubble's parameter $H_{0}$ of our model by minimizing the $\chi^{2}$ through the age differential method, involving a direct measurement of $H$.

Abstract:
In this paper we study the evolution of the equation of state of viscous dark energy in the scope of Bianchi type III space-time. We consider the case when the dark energy is minimally coupled to the perfect fluid as well as direct interaction with it. The viscosity and the interaction between the two fluids are parameterized by constants $\zeta_{0}$ and $\sigma$ respectively. We have made a detailed investigation on the cosmological implications of this parametrization. To differentiate between different dark energy models, we have performed a geometrical diagnostic by using the statefinder pair $\{s, r\}$.

Abstract:
We study the interaction between dark energy (DE) and dark matter (DM) in the scope of anisotropic bianchi type I space-time. First we derive the general form of the dark energy equation of state parameter (EoS) in both non-interacting and interacting cases and then we examine it's future by applying a hyperbolic scale factor. It is shown that in non-interacting case, depending on the value of the anisotropy parameter $K$, the dark energy EoS parameter is varying from phantom to quintessence whereas in interacting case EoS parameter vary in quintessence region. However, in both cases the dark energy EoS parameter $\omega^{de}$, ultimately (i. e at $z=-1$) tends to the cosmological constant ($\omega^{de}=-1$). Moreover, we fixed the cosmological bound on the anisotropy parameter $K$ by using the recent observational data of Hubble parameter.