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): κ_crit = 10⁻⁷⁸ From the Bekenstein bound on the particle horizon. N_accessible ≈ 10⁷⁸ → κ_crit = 1/N_accessible. 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 (d_S: 4 → 2). d_eff = φ × d_S(UV)/d_S(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 = E_Planck × κ_crit^α = 2.50 × 10⁻¹²² M_Pl⁴ 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:• D_V/r_d (z=0.71→1.49): ratio=1.6001 ≈ 8/5=1.6000 (Δ=0.0001, 0.01%)• D_M/r_d (z=0.30→0.71): ratio=1.5914 ≈ 8/5=1.6000 (Δ=0.0054)• D_M/r_d (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═══════════════════════════════════════════════════════════════ final_report.pdf — Complete technical report with all three partsfinal_report.tex — LaTeX source SCRIPTS (self-contained Python, download data automatically): • deep_resolution_ccp.py — Analytical derivation of Λ • percudani_null_hypothesis_test.py — PAR Monte Carlo (±5%) • strict_tolerance_null_test.py — PAR Monte Carlo (±1%) • gw170817_strict_validation.py — GW170817 with ±1% tolerance • refined_methodology.py — Continuous φ-alignment, Fibonacci, adaptive windowing • desi_dr1_exhaustive_phi_analysis.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)