Finslerian gravity extends classical general relativity, enabling a more generalized description of cosmic dynamics. In this study we explore the cosmological evolution of the FLRW model modified by an anisotropic Finslerian parameter (\ (\) ), constructed within the context of Kropina-Barthel spacetime. This spacetime represents a specific class of Finsler geometry that extends Riemannian geometry by incorporating a metric that depends on both the spacetime coordinates and a vector field. Such a formulation provides greater flexibility in modeling spacetime structure, making it particularly valuable for addressing anisotropies in cosmology and investigating the nature of dark energy. This study investigates bouncing cosmology within the framework of Finsler-Kropina geometry by incorporating anisotropic corrections through the geometric function \ ( (t) \). Standard Riemannian cosmological models, which assume isotropy, often result in singularities and do not account for directional dependencies in the early universe. Our Finslerian approach here introduces anisotropy into the spacetime structure, enabling a richer modeling of cosmic evolution. We first obtain the Finslerian Einstein field equations and the energy conservation equation, and explore how anisotropic-effects influence the dynamics of the universe during the bounce phase. Then, using a barotropic equation of state \ (p = (- 1) \) and the form of the scale factor we derive the corresponding form of \ ( (t) \), capturing its role in shaping the anisotropic geometry. Applied to various bouncing models, the results demonstrate that Finslerian parameters ensure stability, regulate energy conditions, and avoid singularities, offering an alternative to inflationary paradigms. Additionally, we develop a new set of cosmographic parameters termed anisotropic cosmographic parameters that extend conventional Hubble, deceleration, jerk, and snap parameters to include the impact of anisotropy. In addition to exploring the Finsler-Kropina framework and its impact on cosmological dynamics, the study incorporates a scalar field description to analyze the interplay between quintessence and phantom fields. The stability of the proposed models is evaluated using perturbation analysis, ensuring their physical viability.
Praveen et al. (Sat,) studied this question.