Anisotropic Dark Energy in 4D Gauss-Bonnet Gravity: Late-Time Cosmology with LRS Bianchi-V Spacetime

This paper examines Locally Rotationally Symmetric (LRS) Bianchi type-V cosmology with a variable Chaplygin gas equation of state, [Formula: see text]. The analysis adopts a late-time, weak-anisotropy approximation, defined by [Formula: see text]; it is not a nonperturbative treatment of arbitrary shear. The field equations used for the dynamical and observational analyses are truncated at the stated perturbative order. Within this regime, the analysis estimates an approximately [Formula: see text] shear suppression relative to General Relativity and identifies an isotropic de Sitter attractor. An MCMC analysis using Hubble-parameter measurements, the Pantheon+ Type Ia supernova sample, and baryon acoustic oscillations gives [Formula: see text] km s[Formula: see text] Mpc[Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. However, the information-criterion comparison does not favor this extended model over [Formula: see text]CDM ([Formula: see text]AIC [Formula: see text] and [Formula: see text]BIC [Formula: see text], defined as the extended-model value minus the [Formula: see text]CDM value). The quoted shear suppression, parameter constraints, model comparisons, and predicted anisotropic imprints ([Formula: see text]) are conditional on [Formula: see text] and should not be extrapolated to strongly anisotropic solutions.