Inhomogeneous Continuum Cosmology and the Hubble Tension: Dynamical Metric-Inertial Expansion in Field-Depleted Environments

The statistically irreconcilable discrepancy exceeding between local late-time determinations of the Hubble constant (; SH0ES/HST) and early-universe measurements inferred from the Cosmic Microwave Background under CDM (; Planck) constitutes the most formidable observational crisis in modern cosmology. In this paper, we demonstrate that the Hubble tension is an inevitable dynamical consequence of treating the universe as an idealized, homogeneous Friedmann-Lemaître-Robertson-Walker (FLRW) metric, whereas the physical cosmos is fundamentally inhomogeneous and governed by the Local Interaction Field Equilibrium (LIFE) continuum framework (). We prove that the effective gravito-inertial expansion rate is directly coupled to local field energy density gradients via Term B-6 (). Observational surveys establish that our local cosmic neighborhood resides inside the Keenan-Barger-Cowie (KBC) void—a significant underdensity spanning approximately 300 Mpc. Within the LIFE framework, destructive field interference inside such underdense regions generates an outward repulsive metric gradient: . This repulsive term imparts an additional outward velocity gradient across the local volume. When properly accounting for this field-theoretic void expansion, the local SH0ES measurement () and the global Planck CMB measurement () converge identically, completely resolving the Hubble tension without exotic relativistic relics or early dark energy. Keywords: Local Interaction Field Equilibrium (LIFE Theory); Hubble Tension; Inhomogeneous Cosmology; KBC Void; Cosmic Expansion; Gravito-Inertial Coupling; Large-Scale Structure.