In this paper, we investigate the bouncing behavior of the universe within the framework of $f(R,L_m)$ gravity, using a simple form of $f(R,L_m)=\frac{R}{2}+L_m^{\gamma }$ (where $\gamma$ 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 ($\omega =-1$) 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 $\gamma$ 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.

在本文中，我们研究了宇宙在以下框架内的弹跳行为：$F(右,L_{米}）$重力，使用简单的形式$F(右,L_{米}）=\frac{右}{2}+L_{米}^{\gamma }$（在哪里$\gamma$是一个自由模型参数）如之前研究的。该模型预测哈勃参数在早期和晚期消失，减速参数在弹跳点接近特定极限。观测到 EoS 参数跨越了虚拟分界线 ($\omega =-1$）在弹跳点附近，表明从收缩阶段到扩张阶段的显着转变。该模型满足成功弹跳场景所需的能量条件，违反表明弹跳点附近存在奇异物质。满足某些值的稳定性条件$\gamma$接近弹跳点，但后期进化中潜在的不稳定性需要进一步研究。最后，我们得出的结论是$F(右,L_{米}）$引力模型对于理解宇宙的动力学很有希望，特别是在弹跳阶段等事件期间。