Observational constraints on a non-polynomial f ( R , T ) gravity model from late-time cosmological probes and statefinder diagnostics

We present observational constraints on the non-polynomial modified gravity model [Formula: see text], where [Formula: see text] denotes the trace of the energy–momentum tensor and [Formula: see text] characterize a non-minimal matter–geometry coupling. Using Bayesian inference with Markov Chain Monte Carlo sampling, we confront the model with late-time cosmological probes including cosmic chronometers, Pantheon+ Type Ia supernovae, and baryon acoustic oscillation measurements from the DESI DR2 compilation. The inclusion of BAO significantly tightens the parameter constraints and drives the modification sector toward values compatible with the General Relativity limit. Geometric diagnostics using the statefinder pair [Formula: see text] and the [Formula: see text] diagnostic indicate quintessence-like effective behavior at low redshift, with trajectories approaching the [Formula: see text]CDM fixed point at higher redshift. The inferred cosmic age remains consistent with bounds from globular clusters. Model comparison based on the Akaike Information Criterion yields only a mild preference for flat [Formula: see text]CDM in the CC+Pantheon+ case, while the inclusion of BAO makes the two models statistically comparable within the Akaike scale. Overall, this functional form remains viable at the background level, although it is not statistically preferred over [Formula: see text]CDM.