Evolution of Brans-Dicke parameter with deceleration parameter within generalized Brans-Dicke theory

In the present work, we have investigated the role of deceleration parameter in the evolution of the Brans-Dicke (BD) parameter. We have considered the generalized Brans-Dicke (GBD) theory where the BD parameter is assumed to be evolving with the the BD scalar field. We have shown that, the GBD theory with a cosmological constant can suitably be expressed as as an effective cosmic fluid within general relativity. We The BD parameter contains two terms one of which may be non-evolving and the other part bears the time evolution. Also, we have shown that, for anisotropic cosmological models within the GBD theory, for the time-independent deceleration parameter, the cosmic anisotropy will not contribute to the evolution of the Brans-Dicke parameter. However, for models with a time-dependent deceleration parameter, the cosmic anisotropy affects the BD parameter as a whole.