Abstract
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–Lemaître–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.
