Time Evolution of the Matter Content of the Expanding Universe in the Framework of Brans-Dicke Gravity

A cosmological model has been constructed in the framework of Brans-Dicke (BD) gravity, based on an inter-conversion between matter and dark energy, for a spatially flat universe in the era of pressureless dust. To account for the non-conservartion of the matter content, a function of time f(t) has been arbitrarily put into the expression of the density of matter. By definition, f(t) is proportional to the matter content of the universe. Using suitable ansazes for scale factor and scalar field, the functional form of f(t) has been determined from the BD field equations. The scale factor has been so chosen that it would cause a signature flip of the deceleration parameter with time. The function f(t) decreases monotonically with time, indicating a transformation of matter into dark energy. Time dependence of the proportions of matter and dark energy of the universe has been determined. The effect of non-conservation of the matter content upon various cosmological parameters has been explored in the present study. Two models of matter-energy interaction have been proposed and f(t) has been expressed as a function of their interaction term. The dark energy equation-of-state (EoS) parameter has been expressed and analyzed in terms of f(t).
Comment: 23 pages, 16 figures, 1 table and 54 equations in the present version. Changes made to the older version: 1)Some errors have been corrected, 2) Three figures have been corrected and their interpretations have been modified, 3) New references have been added, 4) Some explanations have been re-written