Theoretical Models of the Brans-Dicke Parameter for Time Independent Deceleration Parameters

The dependence of the dimensionless Brans-Dicke (BD) coupling parameter upon time and the scalar field has been determined, for an isotropic and homogeneous space of zero curvature, by solving BD field equations and the wave equation for the scalar field. For this purpose, very simple expressions of empirical scale factors, that generate constant deceleration parameters, have been used here in two theoretical models. The characteristics of time dependence of the BD parameter, obtained from these two models, are in qualitative agreement with each other. The mathematical expressions representing the rate of change of the BD parameter with time, based on these two models, are found to have identical forms. Combining the expressions of the BD parameter obtained from these two models, a method for the determination of the present value of the equation-of-state (EoS) parameter of the cosmic fluid has been discussed. Its value is found to be consistent with the ranges of values obtained from other studies based on recent observations