A Study on the Expanding Universe Based on a Model of the Time Variation of its Matter Content in the Framework of Brans-Dicke Theory

TL;DR

This paper develops a theoretical model within Brans-Dicke theory that describes the universe's expansion by considering matter-dark energy conversion, analyzing the variation of matter density, gravitational constant, and deceleration parameter over time.

Contribution

It introduces a novel empirical function for matter density variation in Brans-Dicke cosmology, linking matter content changes with cosmic acceleration and gravitational constant variations.

Findings

Matter converts into dark energy over time.

The model predicts a signature flip in the deceleration parameter.

Variation of gravitational constant is correlated with matter content change.

Abstract

A theoretical model of cosmic expansion has been formulated on an assumption of inter-conversion of matter and dark energy, in the framework of Brans-Dicke theory. An empirical scale factor has been used, which generates a signature flip of the deceleration parameter with time. To account for the non-conservation of matter, a function of time f(t) is incorporated into the equation representing the density of matter. Its value at any instant of time is proportional to the matter content of the universe. The functional form of f(t) has been determined from the field equations by using an empirical scalar field parameter expressed in terms of the scale factor. It is found to decrease with time almost monotonically, implying a conversion of matter into dark energy. Using this function f(t), the time variation of the density of matter has been determined and also the expressions regarding the proportions of matter and dark energy of the universe have been formulated. Time variation of gravitational constant, its fractional rate of change and the Brans-Dicke dimensionless parameter has been analyzed. The dependence of Brans-Dicke parameter upon the scalar field has been determined. The present study enables us to correlate the change of matter content with the change of deceleration parameter and gravitational constant without using any specific mechanism of interaction between matter and scalar field.