Accelerating universe in f(R,Lm) gravity

This paper investigates the dynamics of cosmic expansion within the framework of $f(R,L_m)$ gravity, focusing on the late-time behavior of the universe modeled as a flat Friedmann–Lemaître–Robertson–Walker spacetime. We derive an analytical solution for the field equations and employ advanced statistical techniques, including the Markov Chain Monte Carlo (MCMC) method, to determine best-fit values for the key cosmological parameters, such as the Hubble parameter and the deceleration parameter. Our findings reveal a transition from a decelerating to an accelerating phase of cosmic expansion, aligning closely with observational data as in the $\Lambda$CDM model. The analysis of energy conditions indicates that the strong energy condition is violated, in keeping with the current accelerated expansion of the universe and the nature of dark energy. By elucidating the quintessence behavior of our model through statefinder and Om diagnostics, this study contributes to a deeper understanding of cosmic evolution and the fundamental forces at play. The insights gained pave the way for future research into alternative cosmological models, inviting further exploration of the mysteries surrounding dark energy and the ultimate fate of the universe.