Late time cosmic acceleration through parametrization of Hubble parameter in f(R,Lm) gravity

This paper explores the rapid expansion of the Universe during its later stages within the context of $f(R,L_m)$ gravity theory. We present a novel parametrization of the Hubble parameter in a manner independent of any specific model and employ it to analyze the Friedmann equations within the FLRW Universe framework. Using a Markov Chain Monte Carlo (MCMC) approach, we derive the model parameters by analyzing a composite dataset comprising 31 Cosmic Chronometers (CC) data points, 26 independent Baryonic Acoustic Oscillations (BAO) measurements, and 1701 data points from Pantheon+SH0ES dataset. The trajectory of the deceleration parameter highlights the shift from deceleration to acceleration in the evolution of the Universe. Additionally, we delve into the dynamics of fundamental cosmological variables for two nonlinear $f(R,L_m)$ models, including energy density, pressure, equation of state (EoS) parameter, and energy conditions.