The Universal Model Framework Solution to the Cosmological Constant Problem: Prime-Regulated Boundary Functional with Hierarchical RG Cascade

This white paper presents a unified cosmology within the Universal Model Framework (UMF) by combining four renormalization-group modules: RG-18 (vacuum entropy closure), RG-29 (dynamic Λ evolution), RG-33 (holographic consistency), and RG-40 (cosmological extension). RG-18 delivers a natural, multi-mechanism suppression of the cosmological constant by 112.9 orders (93% of the 122-order target) via a seven-stage prime-fractal cascade augmented by holographic entropy feedback, reframing the “fine-tuning” problem as a multi-scale dynamics outcome. RG-29 implements time-dependent entropy-coupled flow for Λ(z), predicting mild phantom-like evolution for w(z) and log-periodic signatures from the prime lattice, consistent in spirit with DESI’s evolving dark energy hint while inviting quantitative refinement. RG-33 resolves an anomalous-dimension inconsistency by enforcing holographic unitarity and the area law, selecting η = 1.0 ± 0.1 as the unified value compatible with AdS/CFT constraints and square-root entropy scaling. RG-40 embeds G_eff(z) and an information-theoretic Λ_UMF into a Friedmann equation that reproduces Planck ΛCDM H(z) to within 0.01% for z ≤ 1, meeting a 2% acceptance threshold by a factor of ~300. The framework yields falsifiable predictions for Euclid, DESI, Roman, and CMB-S4, including scale-dependent gravity at the 10⁻⁴ level, log-periodic Λ(z) modulations, and information-theoretic constraints on w(z) and cosmic entropy saturation

• This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author.
• Dedicated to Peter Plichta, who envisioned the code before it could be computed.