The Vacuum Displacement Principle: Theoretical Framework and Local Phenomenology

Abstract

We present a modified gravitational framework in which the standard Einstein field equations are sourced by a classical matter sector coupled to a Higgs-type scalar field $\chi$ modeling a dynamic vacuum substrate. By introducing a phenomenological covariant coupling we implement a physical displacement principle where massive baryonic matter drives the vacuum field away from its vacuum expectation value. We show that this coupling leads to a field-dependent modulation of a particle's inertial rest mass alongside a spatial fifth force, yielding localized violations of the Einstein Equivalence Principle while preserving universal free fall for fundamental point masses. In the weak-field, non-relativistic limit, this interaction manifests as a Yukawa-type correction to the Newtonian potential. We test the viability of this framework against local gravitational constraints, including planetary perihelion precession and Eötvös parameter limits. Finally, we model the steady-state, non-relativistic spherical accretion of dust, demonstrating that the competing effects of vacuum-induced mass modulation and fifth-force acceleration yield distinct density and velocity profiles.