Time dependence of Gravitational Constant and Deceleration Parameter in the Framework of Brans-Dicke Theory

Abstract

A simple empirical expression has been chosen to represent the Brans-Dicke (BD) scalar field

as a function
of the scale factor in such a manner that the density of matter ( ) of the universe has the same functional
dependence upon the scale factor. An interaction and a consequent inter-conversion between the matter and
dark energy have been considered in this formulation. The present model is based on the generalized BD theory
where the BD parameter

is regarded as a function of the scalar field

. Solving the field equations for a
spatially flat Robertson-Walker space-time, the functional forms of
at() , qt() , ( ) , ( ) have been
determined and their inter-dependence has been analyzed in detail. The parameter ( ) has been found to have
a negative value. The possibility of an inter-conversion between dark energy and matter has been taken into
account by introducing a slowly varying function ( ). A signature flip of deceleration parameter, implying a
transition from deceleration to acceleration, and an increase of gravitational constant with time, have been
found in the present study. Analytically and also through numerical plots, the time dependence and interdependence of the relevant parameters have been explored.