GAC-Phase-Cosmology (GACPC) v4.2.3: Dynamical Effective Field Theory & Technical Supplement

GACPC v4.2.3 – A Dynamical Effective Field Theory Framework This major release transforms the GAC-Phase-Cosmology (GACPC) from a conceptual model into a rigorous, Dynamical Effective Field Theory (EFT). At its core, the framework introduces Primordial Resonance Damping (PRD) within a manifestly covariant field-interaction structure, modeling cosmic evolution as a primary scalar wavefront interacting with a background medium field χ. The framework provides a physically consistent mechanical solution to the 5σ Hubble tension and the "Impossible Early Galaxy" problem identified by JWST. By coupling microscopic interaction rates to a dynamical background medium, GACPC establishes a bridge between quantum-scale dissipative processes and the macroscopic expansion history of spacetime. Major Updates (v3.0 to v4.2.3): Full Dynamization: Transitioned from static background factors to a dynamic scalar field (χ) representing the medium, ensuring local energy conservation through coupled conservation equations. Manifest Covariance: Implemented a 4-velocity-coupled dissipation term (η(χ)uμ∇μφ) to ensure full Lorentz invariance. Hubble Tension Formalization: Derived a formal correction term (δ H) for the Hubble parameter based on φ → χ energy density transfer, providing a predictable shift in expansion history. Quantitative Scaling: Introduced a vacuum-coupling constant (α ~ 10⁻²) to model accelerated interaction rates (Γ) during the primordial high-frequency phase, directly addressing early galaxy maturity at $z > 10$. Mathematical Hardening: Specified explicit Lagrangians and self-interaction potentials, enabling numerical simulation and rigorous peer-review. Observational Signatures & Falsifiability: The model remains highly testable through precision measurements of the expansion history $H(z)$ and the dark energy equation of state $w(z)$. Key predictions include: A time-dependent $w(z)$ with a potential transient phantom-like phase ($w < -1$). A characteristic peak in the Hubble deviation (δ H) during the intermediate redshift regime (z ~ 1-3). Collaborative Effort: Developed by Andro (Lead) with collaborative AI research and scientific advisory from Gemini, Microsoft Copilot, and ChatGPT.