FRW cosmological models in Brans-Dicke theory of gravity with variable q $q$ and dynamical Λ $\varLambda$ -term

Abstract

Exact solution of modified Einstein’s field equations are considered within the scope of spatially homogeneous and isotropic Fraidmann-Robertson-Walker (FRW) space-time filled with perfect fluid in the frame work of Brans-Dicke scalar-tensor theory of gravity. In this paper we have investigated the flat, open and closed FRW models and the effect of dynamic cosmological term on the evolution of the universe. Two types of FRW cosmological models are obtained by setting the power law between the scalar field $\phi$ and the scale factor $a$ and deceleration parameter (DP) $q$ as a time dependent. The concept of time dependent DP with some proper assumptions yield two type of the average scale factors (i) $a(t)=[\sinh(\alpha t)]^{\frac{1}{n}}$ and (ii) $a(t)=[t^{\alpha}e^{t}]^{\frac{1}{n}}$ , $\alpha$ and $n\neq 0$ are arbitrary constants. In case (i), for $0 < n \leq 1$ , it generates a class of accelerating models while for $n > 1$ , the models of the universe exhibit phase transition from early decelerating to present accelerating phase and the transition redshift $z_{t}$ has been calculated and found to be in good agreement with the results from recent astrophysical observations. In case (ii), for $n \geq 2$ and $\alpha = 1$ , we obtain a class of transit models of the universe from early decelerating to present accelerating phase. Taking into consideration the observational data, we conclude that the cosmological constant behaves as a positive decreasing function of time. The physical and geometric properties of the models are also discussed with the help of graphical presentations.