Generalized ghost dark energy model in Brans–Dicke theory with logarithmic scalar field

We study generalized ghost dark energy model in Brans–Dicke theory within the framework of flat Friedmann–Lemaitre–Robertson–Walker Universe. We assume the well-motivated logarithmic form of Brans–Dicke scalar field in terms of the scale factor to find the observational parameters such as equation of state parameter $w_g$ and deceleration parameter q. It is observed that the equation of state parameter crosses the phantom divide line $(w_g=-1)$ for a suitable range of model parameters. We observe that the deceleration parameter is time-dependent which shows the recent phase transition from decelerated to accelerated expansion of the Universe. Moreover, the model shows that the Universe will go through two future phase transitions, recent accelerated expansion to decelerated expansion and again decelerated expansion to accelerated expansion. We have also plotted the trajectories of the model in the $w_g-w_g^{\prime }$ plane for different values of parameters and explored the freezing and thawing regions. Further, we apply the sound squared speed method to check the stability of the model and found that the model is stable for suitable range of parameters.