Matter bounce cosmology within Finsler-Randers geometry: A comprehensive study of anisotropic influences

In this study, we explore the dynamics of matter bounce cosmology within the framework of Finsler-Randers geometry, focusing on the role of the Finslerian correction term $\eta \left(t\right)$. By integrating Finsler geometry into cosmological models, we introduce anisotropic effects that significantly impact the evolution of the universe, particularly during the bounce phase. The research examines various cosmological parameters, including the deceleration ($q_{\eta }\left(t\right)$), jerk ($j_{\eta }\left(t\right)$), and snap ($s_{\eta }\left(t\right)$) parameters, highlighting the influence of the Finsler correction on these key indicators. Our results demonstrate that the Finslerian framework leads to more complex and abrupt transitions in the universe's expansion dynamics compared to traditional Riemannian models. The study also reveals that the Finslerian correction intensifies the violations of energy conditions, such as the null energy condition (NEC), which are crucial for the occurrence of a successful bounce. Furthermore, the analysis of the squared sound speed $v_s^2$ indicates that the model's stability is highly sensitive to the choice of the Finslerian parameters, with certain configurations leading to instability during the bounce. Our findings underscore the unique contributions of Finsler geometry to cosmological models, offering deeper insights into the behavior of the universe under anisotropic influences and providing a potential avenue for addressing longstanding challenges in cosmology.