Abstract
As new gravitational theories emerge, their ability to explain the dark sector of the universe becomes increasingly important. In this study, we investigate the [Formula: see text] gravity model, which extends the [Formula: see text] and [Formula: see text] frameworks by unifying the Ricci scalar [Formula: see text], the matter Lagrangian [Formula: see text], and the trace of the energy-momentum tensor [Formula: see text] within a single gravitational Lagrangian. Using the functional form [Formula: see text], where [Formula: see text] and [Formula: see text] are constants, we solve the field equations for the Hubble parameter [Formula: see text] with a parametric equation of state [Formula: see text] as a function of redshift [Formula: see text]. The results of our MCMC analysis, based on Hubble and SNe Ia datasets, yield tightly constrained model parameters ([Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]), with the joint dataset reducing uncertainties. The model successfully captures the evolution of the Hubble parameter, deceleration parameter, energy density, and the [Formula: see text] diagnostic, showing a transition from deceleration to acceleration and an eventual de Sitterlike expansion at [Formula: see text]. The [Formula: see text] consistently describes the universe’s expansion across different epochs, reinforcing the validity of the [Formula: see text] gravity model and its ability to replicate key cosmological features.