Time Dependence of Density Parameters for a Variable EoS Parameter in Brans-Dicke Framework

Abstract

The time dependence of the equation-of-state (EoS) parameter has been determined in the framework of the Brans-Dicke (BD) theory, using BD field equations and the wave equation for the scalar field, for a homogeneous, isotropic and spatially flat universe. This study is based on a model where a linear combination of BD field equations has been taken. The generalized expression of the EoS parameter is a function of the ratio of the constant coefficients used for this linear combination. Expressions of the densities of matter and dark energy and also the density parameters for matter and dark energy have been derived in terms of the EoS parameter. The value of the EoS parameter, at the present epoch, is found to depend, almost solely, on a constant that determines the time dependence of the scalar field. This parameter and the ratio of constant coefficients have been varied, to show graphically, the time dependence of the matter density and the density parameters for matter and dark energy. For certain combinations of these parameters, the matter density is found to decrease with time after initially rising to a peak value, indicating generation of matter, probably from dark energy, during an era in the past.