Cosmological model in Finsler-Kropina geometrical framework with weak-field anisotropy and observational data

This study explores the role of Finsler geometry in cosmology incorporating weak-field anisotropy through the Finsler-Kropina framework and the osculating Riemannian metric approach. The model naturally modifies the spacetime structure introducing anisotropic effects that influence cosmic expansion and energy conservation. By deriving the modified Friedmann equations we test their observational viability using observational datasets including cosmic chronometers, baryon acoustic oscillations and the Pantheon+ supernovae dataset. The results from MCMC analysis show deviations from the ΛCDM model particularly in the evolution of the Hubble parameter, matter density, and dark energy density. Compared to ΛCDM, the anisotropic model predicts a lower matter density parameter ${\Omega }_{m0}$ a reduced dark energy density ${\Omega }_{\Lambda }$, and a nonzero spatial curvature ${\Omega }_K$ indicating fundamental geometric differences. The deceleration parameter $q\left(0\right)=-0.57\pm 0.001$ confirms an accelerated expansion with a transition redshift $z_{tr}\approx 0.77$, aligning with observational estimates. The state-finder diagnostics reveal a transition from a Chaplygin gas-like phase to a quintessence regime before asymptotically approaching ΛCDM demonstrating a dynamic evolution influenced by anisotropic corrections. The $Om\left(z\right)$ diagnostic suggests phantom-like behavior at higher redshifts gradually stabilizing towards ΛCDM at late times. We show that the geometry-induced effective dark energy term ${\Omega }_{\xi }$ can be interpreted as a geometric component of dark energy, effectively driving late-time acceleration without invoking additional exotic matter fields. These findings highlight the significance of Finsler geometry in extending standard cosmology and suggest that anisotropic effects provide a geometric interpretation of dark energy while maintaining consistency with observational constraints.