Formulation of Scale-Gauge Theory and Its Cosmological Consequences Part I: Foundational Framework

We propose an extended scale gauge theory that addresses the hierarchy problem and the cosmological constant problem within a unified geometric framework. By introducing a dynamical balance mechanism between scale invariance and vacuum energy, the model provides a natural explanation for the smallness of the cosmological constant. This approach offers a new perspective on the interplay between fundamental constants and the geometry of spacetime, potentially bridging gaps between quantum field theory and cosmology.