A study on the dependence of the dimensionless Brans-Dicke parameter on the scalar field and their time dependence

The present paper reports a study on the dimensionless parameter $\omega$ in Brans-Dicke theory. Based on a particular choice of scale factor $a$, we have investigated the signature flip of the deceleration parameter $q$ to see whether the transition from decelerated to accelerated expansion of the universe is achievable under this choice of scale factor. Restrictions on the parameters obtained for this choice of scale factor have been subsequently used for discussing the Brans-Dicke parameter for two choices of scalar fields $\phi$. Moreover, analytical solutions for the Brans-Dicke parameter without any assumption about the scalar field have been obtained from the modified field equations through the choice of scale factor under consideration. Viable models have been obtained by comparing the results with observations.