Cosmic evolution of Sharma–Mittal holographic dark energy in Brans–Dicke–Rastall gravity

This research explores the cosmological evolution of Sharma–Mittal holographic dark energy in the context of Brans–Dicke–Rastall gravity. Using a correspondence approach, we construct a dark energy model by considering power law of the scalar field of Brans–Dicke–Rastall gravity. The optimal values for the model parameters were determined by fitting our model to the updated Hubble dataset. We conduct a qualitative analysis of the model by examining the evolutionary trajectories of key parameters, such as the dark energy equation of state ([Formula: see text]), statefinder diagnostic parameters [Formula: see text] and the deceleration parameter (q). The findings show that the deceleration value emphasizes a change from a decelerated to an accelerated epoch, whereas the equation of state parameter characterizes a quintom era in the Universe. We further examine the [Formula: see text] plane, which suggests a steady-state scenario in the model’s late-time evolution. We conclude that our universe is around [Formula: see text], which is consistent with the observed data.