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

TL;DR

This paper introduces a modified gravity model with a Higgs-like scalar field that explains galactic rotation curves and cosmological constant issues without dark matter or dark energy.

Contribution

It proposes a novel vacuum displacement principle via a scalar field coupling, leading to testable modifications of gravity at galactic and cosmological scales.

Findings

Recovers Schwarzschild metric in vacuum

Provides Yukawa-like correction to Newtonian potential

Offers a dynamical solution to dark matter and dark energy problems

Abstract

We present a modified gravity framework where the vacuum is modeled as a Higgs-type scalar field $\chi$ undergoing spontaneous symmetry breaking. By introducing a coupling $Q^\nu = \alpha T \nabla^\nu \chi$, we formalize a displacement principle where 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.