Determination of time evolution of the gravitational constant in the framework of Brans-Dicke Theory: An easy wa

Abstract

The present article demonstrates a very simple mathematical way to determine the time-dependence of the dynamical gravitational constant () in the framework of the Brans-Dicke theory of gravity. Brans-Dicke field equations, for a matter-dominated, pressure-less and spatially flat universe with homogeneous and isotropic space-time, have been used for this formulation. The gravitational constant () is the reciprocal of the Brans-Dicke scalar field (). Using a simple ansatz, which represents the Brans-Dicke scalar field () as a function of time, the possible values of a constant parameter (constituting the ansatz) have been calculated with the help of the field equations, using the values of some cosmological parameters at the present time. The values of that parameter (belonging to the ansatz) lead to the conclusion that the scalar field () decreases and consequently the gravitational constant () increases with time. The value of the relative time-rate of change of the gravitational constant (i.e., ) has also been estimated and this quantity has been found to be independent of time. Time-dependence of and has been depicted graphically for all values of the parameter belonging to the ansatz. The novel features of this study are that the gravitational field equations did not have to be solved, unlike other studies, to arrive at the results and the mathematical scheme for calculations is extremely easy in comparison to other recent studies in this regard.