GAC-Phase-Cosmology (GACPC) - Technical Supplement v4.2.3

GACPC v4.2.3 – A Dynamical Effective Field Theory Framework This major update transforms the GAC-Phase-Cosmology (GACPC) from a conceptual model into a formal, Dynamical Effective Field Theory (EFT). At its core, the framework introduces Primordial Resonance Damping (PRD) within a manifestly covariant field-interaction structure. The model provides a mechanical solution to the $5\sigma$ Hubble tension and the "Impossible Early Galaxy" problem identified by JWST. By coupling microscopic interaction rates to a dynamical background medium field ($\chi$), the GACPC establishes a consistent bridge between quantum-scale dissipative processes and the macroscopic expansion of spacetime. This version provides the necessary mathematical foundation for numerical verification and falsification against $\Lambda$CDM. Changelog (v3.0 to v4.2.3) Major Update: Transition to Dynamical EFT Full Dynamization: Shifted from static background envelope factors to a dynamic scalar field ($\chi$) representing the medium, ensuring local energy conservation and consistency with the laws of thermodynamics. Manifest Covariance: Implemented a 4-velocity-coupled dissipation term ($\eta(\chi) u^\mu \nabla_\mu \phi$) to ensure full Lorentz invariance across all relativistic frames. Hubble Tension Formalization: Derived a formal correction term ($\delta H$) for the Hubble parameter based on the $\phi \to \chi$ energy density transfer, providing a predictable shift in expansion history. Quantitative Scaling: Introduced a vacuum-coupling constant ($\alpha \sim 10^{-2}$) to model accelerated interaction rates ($\Gamma$) during the primordial high-frequency phase, directly addressing JWST's early galaxy maturity observations. Mathematical Hardening: Specified explicit Lagrangians and self-interaction potentials ($V(\phi)$, $U(\chi)$), enabling the model for numerical simulation and rigorous peer-review. Collaborative effort by Andro (Lead), Gemini, Copilot and ChatGPT.