Phantom dark energy model in Brans–Dicke theory of gravity with observational constraints

In this paper, we investigate dark energy scenarios in the Brans–Dicke theory of gravity in the Lyra manifold. We find an analytic solution of the field equations for a flat, homogeneous, and isotropic universe in the form of a hyperbolic solution. We made observational constraints on the model solutions using cosmic chronometer (CC) and Pantheon datasets in MCMC analysis. Using these constrained solutions, we investigate the evolution of universe history by investigating the decelerating parameter [Formula: see text], effective equation of state (EoS) [Formula: see text], dark energy EoS [Formula: see text], scalar field [Formula: see text], etc. We also analyze the Om diagnostic and age of the universe. We have measured the current value of the dark energy EoS parameter [Formula: see text] with the deceleration parameter [Formula: see text]. We have found the present age of the universe [Formula: see text] Gyrs with transition redshift [Formula: see text], which is consistent with recent observations. We have obtained a phantom dark energy transit phase-accelerating cosmological model.