Dewhirst Horizon Relation; A Covariant Scalar-Tensor Framework for Dynamic Horizon Scale Modification: Preserving Local Gauge Invariance and Resolving Galactic Rotation Profiles

This paper presents the formal, covariant scalar-tensor expansion of the Einstein-Hilbert action for the Dewhirst Horizon Relation—an alternative gravity framework authored and formulated by Richard Stephen Dewhirst. Bypassing simple, discontinuous step-function mass-multipliers, this monograph introduces a continuous scalar field (φ) that is non-minimally coupled to the Ricci curvature scalar (R). The cosmic vacuum value of this field is dynamically bound to the universal expansion velocity ratio \Omega_D(t) \equiv [R(t)/(c \cdot t)]^2, capturing the macro-structural boundary evolution of the universal horizon across a revised 14.12-billion-year chronological history timeline. At our modern cosmological timestamp, this dimensional balance yields a stable background baseline modifier value of \Omega_D \approx 10.794. To satisfy strict local conservation laws and reconcile this global scaling layer with sub-parts-per-trillion local solar system tracking data, the framework incorporates a density-dependent screening mechanism. In high-density baryonic environments (such as laboratories and planetary systems), the effective mass of the scalar field increases exponentially, suppressing interactions and smoothly forcing φ → 0. This continuous metric transition guarantees that local mass-energy conservation is perfectly preserved and classical relativity (E=mc²) is natively recovered as a C² smooth, differentiable limit in all local inertial frames. Concurrently, across unshielded low-density backgrounds (such as galactic halos and interstellar voids), the screening mechanism relaxes, smoothly activating the global metric scaling potential. Operating entirely with observed baryonic configurations, this self-consistent action naturally reproduces the flat 220 km/s stellar velocity profiles observed in the ESA Gaia galactic registries and maps early universe plasma density wave oscillations directly to the first acoustic power spectrum peak (\ell = 219.8) of the ESA Planck Satellite Cosmic Microwave Background maps, providing a robust, dark-matter-free alternative for large-scale cosmological evolution.