Time Variation of Deceleration Parameter and Gravitational Constant in the Light of Brans–Dicke Theory

Sudipto Roy

Volume : IV, Issue : XI, November - 2015

Time Variation of Deceleration Parameter and Gravitational Constant in the Light of Brans–Dicke Theory

Sudipto Roy

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 (ρ) 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 , , H(t), G(t) have been determined and their inter–dependence has been analyzed in detail. The parameter ω(φ) 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 f(t). 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 inter–dependence of the relevant parameters have been explored.