Spontaneous Symmetry Breaking and the Vacuum Displacement Principle: From Galactic Scales to Cosmic Fine-Tuning

Abstract

We present a modified gravity framework based on a principle of vacuum displacement, where the vacuum is modeled as a Higgs-type scalar field $χ$ undergoing spontaneous symmetry breaking. The macroscopic manifestation of such vacuum displacement principle is phenomenologically introduced via a low-energy effective scalar tensor coupling so that baryonic matter acts as an impurity in the vacuum substrate. This interaction leads to a restorative buoyancy force that modifies the geodesic equation and violates the Weak Equivalence Principle. We show that this mechanism naturally recovers the Schwarzschild metric in the vacuum limit while providing a Yukawa-corrected Newtonian potential in the presence of matter. This correction offers a dynamical explanation for flat galactic rotation curves and a tracking mechanism for the cosmological constant, potentially resolving the coincidence and fine-tuning problems without the need of dark sectors.