Observational Study of the Deceleration Parameter in f(R, Lm) Theory of Gravity

We investigate the implications of the modified gravity theory f(R, L-m) on the cosmological evolution. By examining the nonlinear model f(R, L-m) = R/2+ (alpha R + 1)L-m, we explore the impact of a nonminimal coupling between curvature and matter on the cosmic expansion. Using a parametrized deceleration parameter dependent on the redshift z, we analyze the Friedmann-Lemaitre-Robertson-Walker (FLRW) universe in the f(R, L-m) framework. Through observational constraints derived from Cosmic Chronometers (CC), Type Ia Supernovae (SNIa), and Baryon Acoustic Oscillations (BAO), we perform a detailed comparison with the standard Lambda CDM model. Our results show that the f(R, L-m) model is consistent with observational data, but deviations from the Lambda CDM model emerge in its geometric structure, highlighting the potential of f(R, L-m) gravity in explaining the dark energy and cosmic acceleration.