A Study of the Time Variation of Brans-Dicke Parameter (Ω)

Abstract

The explicit dependence of the dimensionless Brans-Dicke (BD) parameter ( ) upon time and also upon the equation of state (EoS) parameter (γ) has been determined, by solving BD field equations for a space of zero curvature and also the wave equation for the scalar field (φ). Empirical expressions of the scale factor and the scalar field have been used for this purpose. Dependence of the present value of the BD parameter ( ) upon a parameter controlling the time variation of the scalar field has been obtained and shown graphically. Time variation of the BD parameter, for different values of the EoS parameter, characterizing cosmological eras, has been depicted graphically.Copy Right, IJAR, 2016, All rights reserved. …………………………………………………………………………………………………….... Introduction:-It has been confirmed by high precision observational data and their interpretations that the universe has been expanding with acceleration [1]. This accelerated expansion is said to be caused and controlled by an entity, known as dark energy, whose true nature has not yet been determined. In theoretical calculations, this dark energy is often represented by the cosmological constant (Λ), found in General Relativity (GR). Although it accounts for the experimental observations quite well, it has its own limitations [2]. A large number of alternative theoretical models have emerged to explain gravitational observations. The strengths as well as weaknesses of these models can be found in scientific literature [3]. Non-minimally coupled scalar field theories, particularly in the framework of Brans-Dicke (BD) theory, have been found to be highly useful in explaining the phenomenon of accelerated expansion, although they have failed to explain local astronomical experiments. A quintessence scalar field in BD theory has been shown to generate an accelerated expansion of the universe [4]. Introducing a potential term in BD theory, which is a function of BD scalar field, also allows one to predict an accelerated expansion of the universe [5]. There are major shortcomings of these models. Contrary to the recent observations and theoretical requirements, these models show the matter dominated universe to have an ever accelerating expansion [6,7]. The dimensionless parameter ω in BD theory plays a very important role in the prediction of observational results. The local astronomical observations are explained very well by GR and demands a high (a few hundreds) value of ω [8]. In several models in BD theory, the accelerated expansion is found to be generated by a small value of ω, typically of the order of unity. A study has shown that if an interaction of BD scalar field with dark matter is taken into consideration, a generalized BD theory predicts an accelerated expansion even with a high value of ω [9]. In all these studies, either the BD theory is changed to suit the present requirement or a quintessence scalar field is used to generate sufficient acceleration. Only an interaction between the BD scalar field and the dark matter was used to explain obs...