Cosmographic and observational tests of <i>f</i> ( <i>R</i> , <i>L</i> _<i>m</i> ) gravity in the era of DESI DR2

We study the late-time expansion of the universe in the framework of curvature-matter coupling gravity by considering the model [Formula: see text], where [Formula: see text], [Formula: see text], and [Formula: see text] are free model parameters. We assume a spatially flat FLRW universe filled with pressureless matter, derive the modified Friedmann equations, and obtain an exact analytical solution for the Hubble parameter. The solution approaches a de Sitter phase in the asymptotic future for [Formula: see text]. The model parameters are constrained through a Bayesian Markov Chain Monte Carlo analysis using cosmic chronometer [Formula: see text] measurements, the Pantheon+SH0ES Type Ia supernova compilation, DESI DR2 baryon acoustic oscillation observations, and their joint combination. The [Formula: see text] and DESI DR2 datasets favor values of the Hubble constant compatible with early- and intermediate-Universe measurements, whereas Pantheon+SH0ES prefers a larger value consistent with local distance-ladder observations. The joint analysis yields [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], indicating that the model remains close to the general relativistic limit while allowing a small curvature-matter coupling. Moreover, we reconstruct the cosmographic parameters [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], which show the expected transition from decelerated to accelerated expansion, remain consistent with a [Formula: see text]CDM-like expansion history, and converge to constant values in the asymptotic future. These results show that a simple curvature-matter coupling presents a reasonable description of the late-time cosmic expansion while remaining compatible with current cosmological observations.