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 integral d4x-gG(Lm)f2(R) in the Einstein-Hilbert action. To obtain observational constraints, we use an exponential-type fluid-pressure profile p=p0eak characterized by the dimensionless parameter k and parameterize f2(R) as Rn with another dimensionless parameter n. Two additional parameters, alpha and beta in the functional form of G(Lm) 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.