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.
Shukla et al. (Tue,) studied this question.