  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.
