Bouncing behavior in f(R,L_m) gravity: Phantom crossing and energy conditions

In this work, we investigate the bouncing behavior of the universe within the framework of f(R,L_m) gravity, using a simple form of f(R,L_m)=R/2+L_m^γ (where γ is a free model parameter) as previously studied. The model predicts a vanishing Hubble parameter in the early and late times, with the deceleration parameter approaching a specific limit at the bouncing point. The EoS parameter is observed to cross the phantom divide line (ω=-1) near the bouncing point, indicating a significant transition from a contracting to an expanding phase. The model satisfies the necessary energy conditions for a successful bouncing scenario, with violations indicating exotic matter near the bouncing point. Stability conditions are satisfied for certain values of γ near the bouncing point, but potential instabilities in late-time evolution require further investigation. Finally, we conclude that the f(R,L_m) gravity model is promising for understanding the universe's dynamics, especially during events like the bouncing phase.