Cosmological anisotropies with Finsler–Randers geometry and large-scale observations

We investigate a cosmological model grounded in Finsler–Randers geometry introducing anisotropic corrections via the Barthel connection and a redshift-dependent parameter of the form $\eta \left(z\right)=1+nz$. This framework extends standard cosmology by incorporating directional dependencies in spacetime and modifies the evolution of principal cosmological parameters including the Hubble parameter $H\left(z\right)$, deceleration parameter $q\left(z\right)$ and dark energy equation of state $\omega \left(z\right)$. By fitting the model to current Cosmic Chronometers (CC), Baryon Acoustic Oscillations (BAO), and Pantheon+ supernova datasets, we constrain the anisotropy parameter $n$ and obtain updated best-fit values for $H_0$, ${\Omega }_{m0}$, $n$ and ${\omega }_{\mathrm{DE}}$. Our results indicate that the linear anisotropy can lead to non-trivial modifications in cosmic expansion with the predicted Hubble constant $H_0=68.56\pm 0.10$ km/s/Mpc lying between the Planck and SH0ES values, thereby partially alleviating the Hubble tension. This study demonstrates that geometric anisotropy within the Finsler–Randers framework provides a physically motivated extension to $\Lambda$CDM and offers new possibilities of studying outstanding challenges in modern cosmology in Finsler geometric background.