What question did this study set out to answer?

The aim is to resolve the cosmological constant problem using the Unified Applicable Time framework and derive vacuum energy density from fundamental principles.

July 3, 2026Open Access

First-Principles Resolution of the Cosmological Constant Problem: Λ = EPlanck × κcrit^ (φ/2 + 3/4) — Derivation, Physical Foundations, Falsifiable Predictions, and Methodological Lessons

Key Points

The aim is to resolve the cosmological constant problem using the Unified Applicable Time framework and derive vacuum energy density from fundamental principles.
Derived vacuum energy density from three physical inputs: informational, geometric-dimensional, and thermodynamic principles.
Utilized Bekenstein bound and 4×4 coherence matrix for calculations.
Performed extensive statistical calibration and Monte Carlo tests for data validation.
Derived vacuum energy density V₀ = E_Planck × κ_crit^α matching Planck 2018 measurements with ~1% accuracy.
Falsifiable predictions include corrections to black hole entropy and gravitational wave observations by 2035.
Methodological lessons documented from various tested astronomical catalogs, revealing a true false-positive rate of 33.7%.

Abstract

COMPLETE RESEARCH RECORD — ZENODO DEPOSITAuthor: Miguel Ángel PercudaniORCID: 0009-0007-1748-3212 ═══════════════════════════════════════════════════════════════ABSTRACT═══════════════════════════════════════════════════════════════ This work presents a first-principles resolution of the cosmological constant problem within the Unified Applicable Time (UAT) framework. The vacuum energy density is derived from three independent physical inputs, each constrained by distinct principles: PILLAR 1 — INFORMATIONAL: κcrit = 10⁻⁷⁸ Explicit calculation from the Bekenstein bound on the particle horizon (R ≈ 46. 5 Gly) yields Nₐccessible ≈ 10⁷⁸ accessible bits, giving κcrit = 1/Nₐccessible = 10⁻⁷⁸. Uncertainty: ±0. 5 in exponent. PILLAR 2 — GEOMETRIC-DIMENSIONAL: φ/2 = 0. 809017 The complex 4×4 coherence matrix of the 8-phase causal array (kₑarly = 0. 96734 from UAT Lagrangian) yields λₘax ∝ φ = 1. 618034. Combined with LQG spectral dimension flow (dS: 4 → 2): dₑff = dS (UV) × φ / dS (IR) = 2φ/4 = φ/2. PILLAR 3 — THERMODYNAMIC: 3/4 = 0. 750000 Quadratic scaling of the double-well potential V ∝ δ² near its minimum yields equipartition at half-phase: 1 − (1/2) ² = 3/4. (Heuristic derivation; full rigor under investigation. ) These combine to give α = φ/2 + 3/4 = 1. 559017, yielding: V₀ = EPlanck × κcrit^α = 2. 50 × 10⁻¹²² MPl⁴ ρ_Λ ≈ 6. 90 × 10⁻²⁷ J/m³ Matching Planck 2018 (6. 83 ± 0. 08 × 10⁻²⁷ J/m³) with ~1% agreement. No parameters were fitted to the cosmological constant itself. ═══════════════════════════════════════════════════════════════FALSIFIABLE PREDICTIONS═══════════════════════════════════════════════════════════════ • Black hole entropy correction: S = A/ (4ℓ²) − (φ/2) ·ln (A/ (4ℓ²) ) • Hawking radiation suppression: PUAT = (3/4) × PHawking• Golden Dirac comb in gravitational wave ringdown (LISA, 2035) • Testable with: LISA, CTA/LHAASO, Fermi-LAT/HAWC, Euclid/Roman ═══════════════════════════════════════════════════════════════METHODOLOGICAL LESSONS (Documented in Section 5) ═══════════════════════════════════════════════════════════════ This investigation included an extensive exploratory phase whose results were discarded following rigorous statistical calibration: • LIGO/Virgo ringdown search: Null result after Monte Carlo PAR protocol (500 iterations). Signal indistinguishable from noise at ±1% tolerance. • Fibonacci ratio detection in 8 astronomical catalogs (Kepler, Chandra, Fermi, JWST, HST, LISA Pathfinder, Planck, DESI): All results invalidated after Monte Carlo test revealed true false-positive rate of 33. 7% (not the assumed 5%). These methodological lessons are documented as contributions to best practices in astrophysical pattern detection. ═══════════════════════════════════════════════════════════════CONTENTS═══════════════════════════════════════════════════════════════ • FinalReport. pdf — Complete manuscript (15 pages, 2 figures, 2 tables) • FinalReport. tex — LaTeX source• deepᵣesolutionccp. py — Analytical derivation script with: - 4×4 complex coherence matrix diagonalization - kₑarly derivation from Lagrangian constraints - Nₐccessible calculation from Bekenstein bound - Numerical verification of all constants ═══════════════════════════════════════════════════════════════KEYWORDS═══════════════════════════════════════════════════════════════ cosmological constant, dark energy, vacuum energy density, golden ratio, causal coherence, Bekenstein bound, Loop Quantum Gravity, spectral dimension, 8-phase coherence matrix, black hole thermodynamics, Hawking radiation, primordial black holes, gravitational waves, LISA, falsifiable predictions, look-elsewhere effect, Monte Carlo calibration, Unified Applicable Time, UAT framework ═══════════════════════════════════════════════════════════════REFERENCES═══════════════════════════════════════════════════════════════ UAT Framework: DOI: 10. 5281/zenodo. 17729221UCP Constant: DOI: 10. 5281/zenodo. 17718670 ═══════════════════════════════════════════════════════════════LICENSE═══════════════════════════════════════════════════════════════ Creative Commons Attribution 4. 0 International (CC BY 4. 0)

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