arXiv2015
The present study reexamines the recent work of Pradhan et al. (Indian J. Phys. 88: 757, 2014) and obtained general exact solutions of the Einstein's field equations with variable gravitational and cosmological "constants" for a spatially homogeneous and anisotropic Bianchi type-I space-time. To study the transit behaviour of Universe, we consider a law of variation of scale factor $a(t) = \left(t^{k} e^{t}\right)^{\frac{1}{n}}$ which yields a time dependent deceleration parameter $q = - 1 + \frac{nk}{(k + t)^{2}}$, comprising a class of models that depicts a transition of the universe from the early decelerated phase to the recent accelerating phase. We find that the time dependent deceleration parameter is reasonable for the present day Universe and give an appropriate description of the evolution of the universe. For $n = 0.27k$, we obtain $q_{0} = -0.73$ which is similar to observed value of deceleration parameter at present epoch. It is also observed that for $n \geq 2$ and $k = 1$, we obtain a class of transit models of the universe from early decelerating to present accelerating phase. For $k = 0$, the universe has non-singular origin. In these models, we arrive at the decision that, from the structure of the field equations, the behaviour of cosmological and gravitational constants and are related. Taking into consideration the observational data, we conclude that the cosmological constant behaves as a positive decreasing function of time whereas gravitational constant is increasing and tend to a constant value at late time. $H(z)/(1+z)$ data ($32$ points) and model prediction as a function of redshift for different $k$ and $n$ are successfully presented by using recent data (Farooq and Ratra, Astrophys. J. 66: L7, 2013). Some physical and geometric properties of the models are also discussed.