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A theoretical model of cosmic expansion has been formulated on an assumptionof inter-conversion of matter and dark energy, in the framework of Brans-Dicketheory. An empirical scale factor has been used, which generates a signatureflip of the deceleration parameter with time. To account for thenon-conservation of matter, a function of time f(t) is incorporated into theequation representing the density of matter. Its value at any instant of timeis proportional to the matter content of the universe. The functional form off(t) has been determined from the field equations by using an empirical scalarfield parameter expressed in terms of the scale factor. It is found to decreasewith time almost monotonically, implying a conversion of matter into darkenergy. Using this function f(t), the time variation of the density of matterhas been determined and also the expressions regarding the proportions ofmatter and dark energy of the universe have been formulated. Time variation ofgravitational constant, its fractional rate of change and the Brans-Dickedimensionless parameter has been analyzed. The dependence of Brans-Dickeparameter upon the scalar field has been determined. The present study enablesus to correlate the change of matter content with the change of decelerationparameter and gravitational constant without using any specific mechanism ofinteraction between matter and scalar field.

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