We use recent 36 observational Hubble data (OHD) in the redshift range .07 ≤ z ≤ 2.36, the joint light curves (JLA) sample, comprised of 740 type Ia supernovae (SNIa) in the redshift range 0.01 ≤ z ≤ 1.30, and their joint combination datasets to constrain anisotropic Bianchi type I (BI) dark energy model(DE). To estimate model parameters, we used Metropolis-Hasting algorithm to perform Monte Carlo Markov Chain analysis. We also compute the covariant matrix for BI dark energy model considering different datasets to compare the correlation between parameters of the model. To check the acceptability of our fittings, all results are compared with those obtained from 9 year WMAP as well as Planck (2015) collaboration. Our estimations show that at 68% confidence level, the dark energy equation of state (EOS) parameter for JLA data varies in quintessence-phantom region while for OHD and the joint combination of datasets only varies in phantom region. It is found that the current cosmic anisotropy is of order ∼ 10 −3 which imply that OHD and JLA datasets do not put tight constrain on this parameter. The deceleration parameter is obtained as q = −0.46 +0.89+0.36 −0.41−0.37 , q = −0.619 +0.12+0.20 −0.0.095−0.24 , and q = −0.52 +0.080+0.014 −0.046−0.15 for H(z), SNIa, and H(z)+SNIa data respectively.

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 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.

We study the evolution of the dark energy parameter within the scope of a spatially flat and isotropic Friedmann-Robertson-Walker (FRW) model filled with barotropic fluid and dark energy. To obtain the deterministic solution we choose the scale factor a(t) = √ te t which yields a time dependent deceleration parameter (DP). In doing so we consider the case minimally coupled with dark energy to the perfect fluid as well as direct interaction with it.

We present dark energy models in an anisotropic Bianchi type-VI 0 (B-VI 0 ) space-time with a variable equation of state (EoS). The EoS for dark energy ω is found to be time dependent and its existing range for derived models is in good agreement with the recent observations of SNe Ia data (Knop et al. in Astrophys. J. 598:102 2003), SNe Ia data with CMBR anisotropy and galaxy clustering statistics (Tegmark et al. in Astrophys. J. 606:702, 2004b) and latest 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. 180:225, 2009; Komatsu et al. in Astrophys. J. Suppl. 180:330, 2009). The cosmological constant is found to be a positive 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. The physical and geometric aspects of the models are also discussed in detail.

In this paper we study the evolution of the dark energy parameter within the scope of a spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model filled with barotropic fluid and dark energy by revisiting the recent results (Amirhashchi et al. in Chin. Phys. Lett. 28:039801, 2011a). To prevail the deterministic solution we select the scale factor a(t) = √ t n e t which generates a time-dependent deceleration parameter (DP), representing a model which generates a transition of the universe from the early decelerating phase to the recent accelerating phase. We consider the two cases of an interacting and non-interacting twofluid (barotropic and dark energy) scenario and obtained general results. The cosmic jerk parameter in our derived model is also found to be in good agreement with the recent data of astrophysical observations under the suitable condition. The physical aspects of the models and the stability of the corresponding solutions are also discussed.