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 ∫ d⁴x √-g G( 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, α and β 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.