Abstract
In this paper, we investigate the divergence-free parametric form of the deceleration parameter within the simplest non-minimal matter-geometry coupling in [Formula: see text] gravity, where [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of the energy–momentum tensor. Specifically, we consider the linear model [Formula: see text], where [Formula: see text] governs the interaction between matter and geometry. Using this parametric form, we derive the Hubble parameter as a function of redshift [Formula: see text] and incorporate it into the modified Friedmann equations. Constraining the model with OHD and Pantheon data, we obtain precise estimates for [Formula: see text], the present deceleration parameter [Formula: see text], and its evolutionary component [Formula: see text], confirming a smooth transition between cosmic deceleration and acceleration. Further, we analyze the evolution of the energy density [Formula: see text] and total EoS parameter [Formula: see text] for different [Formula: see text] values, highlighting deviations from [Formula: see text]CDM and the role of [Formula: see text] in shaping cosmic dynamics. In addition, we examine energy conditions, finding that the NEC and DEC are satisfied throughout evolution, while the SEC is violated at late times, supporting the observed acceleration. Our findings demonstrate that this divergence-free parameterization within [Formula: see text] gravity offers a viable framework for explaining late-time cosmic acceleration while maintaining key observational and theoretical constraints.