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 $\int d^{4}x\sqrt{-g}\mathcal{G}({\mathcal{L}}_m)f_2(R)$ in the Einstein-Hilbert action. To obtain observational constraints, we use an exponential-type fluid-pressure profile $p=p_0{e}^{ak}$ characterized by the dimensionless parameter $k$ and parameterize $f_2(R)$ as $R^n$ with another dimensionless parameter $n$. Two additional parameters, $\alpha$ and $\beta$ in the functional form of $\mathcal{G}({\mathcal{L}}_m)$ 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.