MCMC constraints on dark sector dynamics in f(R,Lm,T) modified gravity

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.