The Kinemetric-Extended Field Equations (KEFE): An Effective Field Theory of Vacuum Rheology and Cosmological Evolution

Version 5-02 (Updated May 4, 2026) (see appendix B for changes with respect to 4-02 and intermediate versions) Abstract Motivated by phenomenological challenges across disparate energy scales - from cosmological H0 and S8 tensions to precision metrology - this paper introduces the Kinemetric-Extended Field Equations (KEFE). The framework models the quantum vacuum, or Zero-Point Field (ZPF), as a macroscopic, relativistic, elastoviscoplastic continuum, representing elementary particles as topologically protected localized resonances (solitons) governed by causal Müller-Israel-Stewart (MIS) hydrodynamics. Formulated as an Effective Field Theory (EFT), the continuum description is explicitly bounded: at the ultraviolet (UV) limit by the spatial Singularity Barrier and the vacuum's cohesive yield limit, which avoids classical infinite-density singularities; and at the infrared (IR) limit by the causal Hubble horizon. Within these domains, inertial mass and macroscopic gravity are modeled as reactive visco-elastic drag forces constrained by the vacuum's finite Maxwell relaxation time and transverse acoustic horizon c. Effective inertial mass is treated not as an immutable scalar, but as a dynamic quantity governed by a tensor-valued visco-elastic coupling field. Evaluating the Bianchi identity constraints on this dynamic coupling implies that localized bare matter is not strictly conserved in isolation. Spatial and temporal gradients in the vacuum state generate an active thermodynamic energy exchange with the continuum, manifesting phenomenologically as an effective non-geodesic fifth force. This force remains null under normal Solar System conditions, maintaining consistency with precision tests of the Weak Equivalence Principle and planetary ephemerides. However, in the extreme low-acceleration regime characteristic of galactic outskirts, the framework predicts the manifestation of this force, reproducing the effects of Modified Newtonian Dynamics (MOND). This topo-elastic approach provides a geometric framework for evaluating fundamental parameters, yielding a derivation of the strong-force mass gap and the bare electron mass via a topological Dirac-Eddington-Zeldovich scaling relation. Temporally, the framework addresses the H0 and S8 tensions through early-universe Thermal-Inertial Feedback (TIF) and late-time visco-elastic relaxation, offering a continuum-thermodynamic alternative to dark sectors. The framework yields predictions testable at accessible energy scales, proposing terrestrial metrology experiments - such as variable-field magnetic bottles, macroscopically sheared cryogenic Penning traps and boundary-layer atom interferometry - to empirically probe the predicted visco-elastic rheology of the vacuum. Ultimately, this work provides a rigorous conceptual translation from abstract geometric spaces to physical rheological ones, establishing testable phenomenological boundaries for topological quantization and emergent gravity.