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

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.
Comment: 14 pages, 8 figures