The general form of the anisotropy parameter of the expansion for Bianchi type-III metric is obtained in the presence of a single diagonal imperfect fluid with a dynamically anisotropic equation of state parameter and a dynamical energy density in general relativity. A special law is assumed for the anisotropy of the fluid which reduces the anisotropy parameter of the expansion to a simple form (
 $${\Delta\propto H^{-2}V^{-2}}$$
 , where Δ is the anisotropy parameter, H is the mean Hubble parameter and V is the volume of the universe). The exact solutions of the Einstein field equations, under the assumption on the anisotropy of the fluid, are obtained for exponential and power-law volumetric expansions. The isotropy of the fluid, space and expansion are examined. It is observed that the universe can approach to isotropy monotonically even in the presence of an anisotropic fluid. The anisotropy of the fluid also isotropizes at later times for accelerating models and evolves into the well-known cosmological constant in the model for exponential volumetric expansion.

Bianchi type III models with anisotropic dark energy

New dark energy models in anisotropic Bianchi type-I (B-I) space-time with variable EoS parameter and constant deceleration parameter have been investigated in the present paper. The Einstein's field equations have been solved by applying a variation law for generalized Hubble's parameter in B-I space-time. 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 equation of state (EoS) parameter $\omega$ is found to be time dependent and its existing range for this model is in good agreement with the recent observations of SNe Ia data, SNe Ia data (with CMBR anisotropy) and galaxy clustering statistics. The cosmological constant $\Lambda$ is found to be a decreasing function of time and it approaches a small positive value at late time (i.e. the present epoch) which is corroborated by results from recent supernovae Ia observations.

Bianchi Type-I Anisotropic Dark Energy Models with Constant Deceleration Parameter

A new dark energy model in anisotropic Bianchi type-I (B-I) space-time with time dependent equation of state (EoS) parameter and constant deceleration parameter has been investigated in the present paper. The Einstein’s field equations have been solved by applying a variation law for generalized Hubble’s parameter (Berman in Il Nuovo Cimento B 74:182, 1983) which generates two types of solutions, one is of power-law type and other is of the exponential form. The existing range of the dark energy EoS parameter ω for derived model is found to be in good agreement with the three recent observations (i) SNe Ia data (Knop et al. in Astrophys. J. 598:102, 2003), (ii) SNe Ia data collaborated with CMBR anisotropy and galaxy clustering statistics (Tegmark et al. in Astrophys. J. 606:702, 2004) and (iii) a combination of cosmological datasets coming from CMB anisotropies, luminosity distances of high redshift type Ia supernovae and galaxy clustering (Hinshaw et al. in Astrophys. J. Suppl. Ser. 180:225, 2009 and Komatsu et al. in Astrophys. J. Suppl. Ser. 180:330, 2009). The cosmological constant Λ is found to be a decreasing function of time and it approaches a small positive value at the present epoch which is corroborated by results from recent supernovae Ia observations. It has also been suggested that the dark energy that explains the observed accelerating universe may arise due to the contribution to the vacuum energy of the EoS in a time dependent background. Geometric and kinematic properties of the model and the behaviour of the anisotropy of the dark energy have been carried out.

Bianchi Type-I Anisotropic Dark Energy Model with Constant Deceleration Parameter

In this paper we study the evolution of the dark energy parameter within the scope of a spatially homogeneous and isotropic FRW universe filled with barotropic fluid and dark energy. The scale factor is considered as a power law function of time which yields a constant deceleration parameter. We consider the case when the dark energy is minimally coupled to the perfect fluid as well as direct interaction with it. The cosmic jerk parameter in our derived models is consistent with the recent data of astrophysical observations. It is concluded that in non-interacting case, all the three open, close and flat universes cross the phantom region whereas in interacting case only open and flat universes cross the phantom region. We find that during the evolution of the universe, the equation of state (EoS) for dark energy ωD changes from ωD>−1 to ωD<−1, which is consistent with recent observations.

An interacting and non-interacting two-fluid scenario for dark energy in FRW universe with constant deceleration parameter

The present study deals with a spatially homogeneous and anisotropic Bianchi type-I (B-I) cosmological models representing massive strings in normal gauge for Lyra’s manifold by applying the variation law for generalized Hubble’s parameter that yields a constant value of deceleration parameter. 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-law type. Using these two forms, Einstein’s modified 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, P.S.: 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 $\sigma^{1}_{~1}$ of the shear tensor $\sigma^{j}_{~i}$. 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. It has been found that the displacement vector β behaves like cosmological term Λ in the normal gauge treatment and the solutions are consistent with recent observations of SNe Ia. It has been found that massive strings dominate in the both decelerating and accelerating universes. The strings dominate in the early universe and eventually disappear from the universe for sufficiently large times. This is in consistent with the current observations. Some physical and geometric behaviour of these models are also discussed.

Anisotropic Bianchi Type-I String Cosmological Models in Normal Gauge for Lyra’s Manifold with Constant Deceleration Parameter

We investigate Bianchi type V cosmological models with bulk viscous fluid source. Exact solutions of the Einstein field equations are presented via a suitable power law assumption for the Hubble parameter. We show that the corresponding solutions retain the well established features of the standard cosmology and in addition, are in accordance with recent type Ia supernovae observations. Some observational parameters for the models have also been discussed.

P. S. Baghel

Papers

Bianchi Type V Cosmological Models with Constant Deceleration Parameter in General Relativity