Observational constraints and cosmological evolution in Finsler Barthel–Kropina space-time

Finslerian gravity provides a compelling extension to standard cosmology by allowing for direction-dependent effects in the structure of space-time. In this study we analyze the cosmological evolution of a modified FLRW universe with an anisotropic parameter modeled with a linear redshift dependence within the Barthel–Kropina Finsler framework. We consider two models for dark energy: Model-1, which assumes a constant dark energy equation of state parameter ( ω de = constant ω de = constant ) and Model-2, which adopts a redshift-evolving CPL form ω de(z) = ω ₀ + ω ₁ z/1+z ω de ( z ) = ω 0 + ω 1 z 1 + z . Using observational data from cosmic chronometers (CC), baryon acoustic oscillations (BAO) and Pantheon + Supernovae we perform parameter estimation with Markov Chain Monte Carlo techniques and analyze cosmographic quantities. Our analysis of the deceleration parameter confirms the presence of late-time cosmic acceleration, consistent with observations. Both Finslerian models yield statistical fits to the data that are comparable to those of the standard Λ Λ CDM cosmology. Model-1 yields statistical results comparable to those of Λ Λ CDM in both AIC and BIC analyses. Model-2, with its evolving dark energy equation of state allows for a more flexible description of late-time cosmic acceleration. Under current observational constraints both models describes the late-time anisotropy and offer a framework to explore deviations from cosmic isotropy beyond the standard cosmological constant scenario.