Late-Time Cosmological Evolution in f(R,ℒm) Gravity with a Matter-Dominated Background

The present study explores the late-time accelerated expansion of the universe and the evolution of cosmic structures in the context of a particular [Formula: see text] gravity model—an extended gravitational framework in which the standard Einstein–Hilbert action is generalized by incorporating a nonlinear coupling between spacetime curvature and matter fields. The specific form of the gravitational action is chosen as [Formula: see text] where [Formula: see text] and [Formula: see text] are free model parameters, and the corresponding equations of motion are derived assuming a matter-dominated cosmological condition. The study is formulated for a spatially flat FLRW universe, where we derive an exact analytical solution to the field equations. We constrain the model parameters using advanced Markov Chain Monte Carlo techniques, employing a combined dataset of BAO, cosmic chronometers, and standard candles. Furthermore, we examine the behavior of physical parameters that describe the various phases of cosmic evolution, including the deceleration parameter [Formula: see text], jerk [Formula: see text], and snap [Formula: see text] parameters and also the statefinder pairs ([Formula: see text]) and ([Formula: see text]). We determine the transition redshift at which the cosmic expansion shifts from decelerating to accelerating, with a resulting value of [Formula: see text]. Statefinder diagnostics show that the [Formula: see text] model follows a simple trajectory, lies in the quintessence region. These findings underscore the significance of [Formula: see text] gravity in explaining cosmic acceleration, without requiring a cosmological constant, and offering a promising framework for future explorations of dark energy and the evolution of the universe.