Observational constraints on generic models of non-minimal curvature-matter coupling

We investigate two classes of non-minimally coupled curvature-matter models in the FLRW Universe with a perfect fluid and analyze their cosmological implications using Supernova Ia, observed Hubble data, and baryon acoustic oscillation measurements. Non-minimal coupling is introduced via an additional term in the Einstein–Hilbert action. To obtain observational constraints, we use an exponential-type fluid-pressure profile characterized by the dimensionless parameter k and parameterize as Rn with another dimensionless parameter n. Two additional parameters, α and β in the functional form of determine the coupling strength. We identify significant regions in the (n, k)-parameter space for fixed coupling strength values where non-minimally coupled models align with observed late-time cosmic evolution. Additionally, we explore and discuss features of energy transfer between the curvature and matter sectors using observational data.