Scalar Field Reconstruction and Anisotropic Evolution of Barrow Holographic Dark Energy in Bianchi Type-V Spacetime

This research investigates the cosmological trajectory of the late-time universe within the framework of modified gravity, specifically incorporating Barrow Holographic Dark Energy (BHDE). By adopting the Hubble horizon as the cosmic infrared cut-off, we derive the modified Friedmann equations influenced by the Barrow exponent). This quantum-gravitational exponent (∆) effectively accounts for the intricate, fractal-like deformations of the black hole event horizon inspired by quantum gravity principles. To establish a robust theoretical connection with mainstream dark energy frameworks, we perform a formal mathematical correspondence and reconstruction between the BHDE model and standard scalar field descriptions, specifically focusing on quintessence, k-essence, and dilaton field paradigms. Unlike conventional isotropic studies that rely entirely on standard homogeneous models, we explore these evolutionary dynamics within an anisotropic Bianchi Type-V spacetime framework. This approach allows us to critically analyze how early-universe initial anisotropy influences or persists into late-time cosmic acceleration. To rigorously determine the physical viability and stability of the reconstructed scalar potentials, we systematically evaluate the classical Energy Conditions, including the Null, Weak, and Strong Energy Conditions. Furthermore, we utilize Statefinder diagnostic parameters {r, s} to distinctly differentiate this modified holographic model from the standard concordance Lambda Cold Dark Matter (ΛCDM) paradigm. Our final results focus on identifying the stable, physically permissible parameter space for the Barrow exponent(∆) that guarantees a smooth topological transition from an early decelerated phase to a perpetually accelerating FLRW universe. Ultimately, this comprehensive study provides a rigorous mathematical bridge between modified spacetime geometry, quantum-corrected horizon thermodynamics, and the underlying holographic nature of the dark sector.