A Model of Time Dependent Equation-of-State Parameter in the Framework of Brans-Dicke Theory

Abstract

The characteristics of a time varying equation-of-state (EoS) parameter have been determined on the basis of a simple model, using Brans-Dicke (BD) field equations for an isotropic and homogeneous universe of spatial curvature zero. The scale factor, scalar field and the dimensionless BD parameter have been represented by empirical expressions assumed for the present study. The scale factor has been so chosen that it would generate a time dependent deceleration parameter showing a signature flip, indicating a change of phase from deceleration to acceleration. Expressions, representing the time dependence of the density of matter, EoS parameter and the BD parameter, have been derived. The nature of time dependence of all these cosmological parameters have been found to depend upon an empirically chosen constant parameter whose value governs the dependence of the scalar field upon the scale factor. For larger values of this parameter, the EoS parameter increases with time approaching a constant negative value and, for more negative values of that constant parameter the EoS parameter decreases with time at a gradually decreasing rate. There are cases where the density of matter initially increases with time to attain a peak value before beginning to fall at a gradually decreasing rate.