Observational Study of the Deceleration Parameter in $$\boldsymbol{f(R,L_{m})}$$ 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–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.