The consequence of higher-order curvature-based constraints on $ f(R, L_m) $ gravity

In this investigation, we perform an observational statistical analysis in the theory of $f(R, L_m)$ gravity. The proposed theoretical model is based on the Ricci scalar's non-linear contribution. We use a distinct parameterization for the deceleration parameter and constrain the model parameters by using various observational data. To determine the best-fit model for the cosmological parameters, we use different observational datasets such as the Hubble Space Telescope, the Pantheon Supernova Survey, the Gold dataset, the Gamma-Ray Burst (GRB), and the Baryon Acoustic Oscillations (BAO). Furthermore, we study the late-time cosmic evolution of the Universe in detail and examine the implications of the constraint values on cosmological parameters. Additionally, we conduct a thorough comparison with the standard cosmological model $\Lambda$CDM and other standard models obtained by Odintsov et al. \cite{Odintsov:2023cli, Odintsov:2024lid} to examine the validity of our proposed model in the low-redshift regimes. Finally, we find that the proposed model encapsulates an intriguing transition from early deceleration at high redshift to acceleration at low redshift, a quintessence dark energy scenario, and convergence towards the well-established $\Lambda$CDM model in late-time Universe's evolution.