Bouncing cosmology and the dynamical stability analysis in f(R,Lm)-gravity

We study the bouncing cosmology in the $f(R,L_m)$ theory of gravity. In this model, we consider a specific function of $f(R,L_m)$ which contains the higher order curvature term along with the matter Lagrangian. Here, we parameterize the Hubble parameter with the motivation that it creates a model with bouncing behavior and solves the initial singularity problem during the universe's early evolution. This model achieves a bounce instead, where the universe rapidly contracts and then quickly expands again. The EoS parameter crosses the quintom line in the vicinity of the bouncing position indicating significant changes in the energy density, isotropic pressure, and temperature in the model. The model is highly unstable near the bouncing point. Finally, we analyze the model's dynamic stability in the neighborhood of the bouncing point by examining the sound velocity and the adiabatic index depictions.