Phase-space structure and stability analysis in f ( R , L m , T ) gravity

This work explores the cosmological dynamics of the Universe within the framework of the modified gravity model Formula: see text using the dynamical system approach. By defining two dimensionless variables, an autonomous system is constructed to analyze the model’s expansion behavior. Three critical points are identified and examined their stability, deceleration parameter, and effective EoS. The point Formula: see text represents a matter-dominated and decelerated phase that is either unstable or saddle-type, while Formula: see text denotes a stable de-Sitter attractor describing the late-time accelerated expansion. The third point, Formula: see text, corresponds to a general phase allowing transitions between quintessence, phantom and de-Sitter regimes depending on model parameters. The present model gives Formula: see text and Formula: see text, with corresponding transition redshifts Formula: see text and Formula: see text for the matter-like and radiation-like configurations, respectively, thereby confirming the existence of a stable late-time accelerating attractor. Moreover, the effective EoS attains Formula: see text and Formula: see text in the two cases, which lies in the quintessence region and supports the present accelerated expansion. The Statefinder analysis further shows that point Formula: see text reproduces the Formula: see textCDM model, whereas point Formula: see text can reduce to it for specific parameter combinations. The statefinder analysis provides Formula: see text and Formula: see text for the matter-like and radiation-like configurations, respectively, suggesting Chaplygin gas-like and quintessence-like late-time dark energy behaviour with mild deviations from the Formula: see textCDM fixed point. Overall, the model effectively unifies standard and dynamical dark energy behaviors within a consistent cosmological framework.