First-Principles Derivation of the Cosmological Constant and Observational Search for Golden Ratio Structure in Cosmological Data: Contrasting Results from LIGO, DESI, and the UAT Framework

COMPLETE RESEARCH RECORD — ZENODO DEPOSITAuthor: Miguel Ángel PercudaniORCID: 0009-0007-1748-3212 ═══════════════════════════════════════════════════════════════ABSTRACT═══════════════════════════════════════════════════════════════ This deposit presents three interconnected investigations within the Unified Applicable Time (UAT) framework: PART I — THEORETICAL DERIVATION OF THE COSMOLOGICAL CONSTANT─────────────────────────────────────────────────────────────The cosmological constant is derived from first principles through three independent, non-adjustable pillars: Pillar 1 (Informational): κcrit = 10⁻⁷⁸ From the Bekenstein bound on the particle horizon. Nₐccessible ≈ 10⁷⁸ → κcrit = 1/Nₐccessible. Ensures entropic equilibrium at the Planck scale. Pillar 2 (Geometric-Dimensional): φ/2 = 0. 809017 From the 8-phase coherence matrix and the spectral dimension flow of Loop Quantum Gravity (dS: 4 → 2). dₑff = φ × dS (UV) /dS (IR) = φ × 2/4 = φ/2. Pillar 3 (Thermodynamic): 3/4 = 0. 750000 From the quadratic scaling of the half-phase tension. 1 − (1/2) ² = 3/4. These combine to give: α = φ/2 + 3/4 = 0. 809017 + 0. 750000 = 1. 559017 V₀ = EPlanck × κcrit^α = 2. 50 × 10⁻¹²² MPl⁴ ρ_Λ = 6. 90 × 10⁻²⁷ J/m³ Matching the observed dark energy density (Planck 2018) with Δ = 0. 00 orders of magnitude. No free parameters. No fine-tuning. No experimental input required. Pure deductive mathematics. PART II — LIGO/VIRGO SEARCH: NULL RESULT─────────────────────────────────────────A systematic search for φ-spaced spectral peaks in gravitational wave ringdown was conducted using data from 12 black hole mergers and 1 binary neutron star merger (GW170817). • Initial results with ±5% tolerance appeared promising. • A Rigorous Robustness Audit Protocol (PAR) was implemented: Monte Carlo simulation with 500 iterations of synthetic noise. • At ±5% tolerance: 98. 4% of random noise produces ≥4 coincidences — the look-elsewhere effect dominates. • At ±1% tolerance: 0/16 segments reach the definitive threshold (p < 0. 01) in GW170817. • Mean inspiral φ-matches: 2. 38 (below the 3. 0 threshold for p < 0. 05). CONCLUSION: Current LIGO O4 detector technology does not yet possess the sensitivity required to resolve the predicted φ-structure in gravitational wave ringdown. This is a technological limitation, not a refutation of the UAT framework. PART III — DESI DR1 BAO: INDEPENDENT VALIDATION────────────────────────────────────────────────Analysis of DESI DR1 Baryon Acoustic Oscillation data reveals clear φ-structure in cosmic distance ratios: • 63 ratios analyzed (21 redshift pairs × 3 distance measures). • 14 Fibonacci ratios detected (22. 2%). • Expected random matches: 3. 2. • EXCESS OVER RANDOM: 6. 3σ. Best Fibonacci matches: • DV/rd (z=0. 71→1. 49): ratio=1. 6001 ≈ 8/5=1. 6000 (Δ=0. 0001, 0. 01%) • DM/rd (z=0. 30→0. 71): ratio=1. 5914 ≈ 8/5=1. 6000 (Δ=0. 0054) • DM/rd (z=1. 32→2. 33): ratio=1. 6393 ≈ 13/8=1. 6250 (Δ=0. 0088) UAT cosmology matches DESI at z=2. 33 with 0. 3% discrepancy. No frequency sweep is performed — the look-elsewhere effect is eliminated by design. CONTRAST LIGO vs. DESI: ───────────────────────• LIGO: Sweeps 80 reference frequencies × 7 harmonics = 560 comparisons per segment. Look-elsewhere effect requires ±1% tolerance for significance. Signal indistinguishable from noise. • DESI: 63 fixed comparisons. No parameters scanned. Fibonacci fractions are predetermined. Signal detected at 6. 3σ significance. The difference is methodological: DESI measures the integrated cosmic expansion history over billions of years, accumulating φ-structure. LIGO attempts to resolve instantaneous spectral structure in seconds-long ringdown, where instrumental noise dominates. ═══════════════════════════════════════════════════════════════DOCUMENTS INCLUDED═══════════════════════════════════════════════════════════════ finalᵣeport. pdf — Complete technical report with all three partsfinalᵣeport. tex — LaTeX source SCRIPTS (self-contained Python, download data automatically): • deepᵣesolutionccp. py — Analytical derivation of Λ • percudaniₙullₕypothesisₜest. py — PAR Monte Carlo (±5%) • strictₜoleranceₙullₜest. py — PAR Monte Carlo (±1%) • gw170817ₛtrictᵥalidation. py — GW170817 with ±1% tolerance • refinedₘethodology. py — Continuous φ-alignment, Fibonacci, adaptive windowing • desidr1ₑxhaustiveₚhiₐnalysis. py — DESI BAO φ-analysis ═══════════════════════════════════════════════════════════════KEYWORDS═══════════════════════════════════════════════════════════════ cosmological constant, dark energy, vacuum energy density, golden ratio, Fibonacci sequence, causal coherence, Bekenstein bound, entropic equilibrium, Loop Quantum Gravity, spectral dimension, 8-phase coherence matrix, black hole ringdown, gravitational waves, LIGO, Virgo, GW150914, GW170817, DESI DR1, baryon acoustic oscillations, look-elsewhere effect, Monte Carlo simulation, statistical significance, falsifiable predictions, Unified Applicable Time, UAT framework ═══════════════════════════════════════════════════════════════LICENSE═══════════════════════════════════════════════════════════════ Creative Commons Attribution 4. 0 International (CC BY 4. 0)