A Theoretical Study of the Cosmic Expansion in the Framework of Brans-Dicke Theory

Abstract

On the basis of an assumption of inter-conversion of matter and dark energy, a theoretical model of cosmic expansion has been formulated, in the framework of Brans-Dicke (BD) theory. Empirical expressions of scale factor (�� ) and scalar field parameter (�� ) have been used. The scale factor is such that it generates a signature flip of the deceleration parameter with time. A function of time �� (�� ), defined in terms of the density of matter (�� ), is used to account for the non-conservation of matter. This function is proportional to the matter content of the universe. Using an empirical scalar field parameter, in terms of scale factor, the functional form of �� (�� ) has been determined from the BD field equations. The present study reveals that �� (�� ) decreases with time, indicating a conversion of matter into dark energy. Based on this function, the time variation of the density of matter (�� ) has been determined. Expressions regarding the proportions of matter and dark energy of the universe have been derived. The time dependence of gravitational constant (�� ), �� �� and the BD dimensionless parameter ��(�� ) have been explored. The functional dependence of BD parameter ��(�� ) upon the scalar field (�� ) has been formulated. The study based on the present model establishes a correlation between the transformation of matter content into dark energy and the change of cosmological parameters connected to cosmic expansion, without employing any particular model of interaction between scalar field and matter. Keywords: Cosmology, Brans-Dicke parameter, Scalar field, Conversion of matter into dark energy, Time varying gravitational constant, Accelerated expansion of the universe.