Investigating late-time cosmology using Finsler-Randers geometry and Barthel connection: Observational constraints and implications

In this study we explore cosmological anisotropies and dark energy using Finsler-Randers geometry, an extension of Riemannian geometry that incorporates directional dependence in the spacetime structure. We investigate whether Finslerian modifications including anisotropic corrections can provide a unified theoretical framework to explain both the observed cosmic acceleration and the anisotropies detected in the Cosmic Microwave Background and large-scale structure surveys. By introducing an anisotropic parameter η(t) with its parametrization we study its impact on cosmological models and compare the results with observational data from Cosmic Chronometers (CC), Baryon Acoustic Oscillations (BAO), and the Pantheon+ Type Ia Supernovae sample. The constraints on key cosmological parameters including the Hubble constant H0, matter density parameter Ωm, and the anisotropic parameter n, are derived using a Markov Chain Monte Carlo (MCMC) method. Our findings suggest that Finsler-Randers geometry provides a viable alternative to the standard ΛCDM model offering new insights into the nature of DE and large-scale anisotropies. We also examine the consistency of the anisotropic term n across different datasets evaluating its implications for both the evolution of the universe and potential deviations from isotropy. The results highlight the relevance of Finslerian geometry in cosmology and its potential to resolve some of the longstanding puzzles in contemporary cosmology.