Cosmological dynamics in f(R,T) gravity theory with a linear equation of state parameterization

We investigate a cosmological model within the framework of [Formula: see text] gravity by adopting the linear functional form [Formula: see text], where [Formula: see text] denotes the matter-geometry coupling constant. Working within a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) background, we derive the modified Friedmann equations and subsequently obtain an analytical expression for the Hubble parameter by employing a linear redshift-dependent parameterization of the equation of state (EOS), [Formula: see text]. The model parameters are constrained through a comprehensive multi-dataset observational analysis utilizing cosmic chronometer (CC) measurements, Type Ia supernovae data from the Pantheon+ and Union 3.0 compilations, baryon acoustic oscillation (BAO) data from the DESI survey, and cosmic microwave background (CMB) distance priors derived from Planck 2018 observations. Best-fit parameter values are extracted via [Formula: see text] minimization over the combined dataset as well as individual dataset separately. We explore the cosmological evolution of the model through several physical diagnostics, including the effective energy density, cosmic pressure, EOS parameter, and deceleration parameter. Higher order geometrical diagnostics, such as the statefinder pair [Formula: see text], the jerk parameter [Formula: see text], and the [Formula: see text] diagnostic, all are utilized to differentiate the presented model from the standard [Formula: see text]CDM framework. Our critical analysis describes that the model successfully could exhibits the transition from an early decelerating phase to the present epoch of accelerated expansion of the Universe, with an EOS parameter lying within the quintessence domain. An overall testing of the energy conditions confirms their validity in the allowed parameter space.