What question did this study set out to answer?

This research aims to resolve the cosmological constant problem, addressing the significant discrepancy in vacuum energy density predictions.

June 30, 2026Open Access

Complete Resolution of the Cosmological Constant Problem within the Unified Applicable Time (UAT) Framework: From 10¹²² to Exact Closure via the Causal Coherence Constant κcrit, the Golden Ratio φ, and Spacetime Information Theory

Key Points

This research aims to resolve the cosmological constant problem, addressing the significant discrepancy in vacuum energy density predictions.
Utilized the Unified Applicable Time (UAT) framework to derive solutions in three stages.
Applied Lagrangian reduction and causal closure principles to examine vacuum energy density.
Tested four independent hypotheses to derive the fundamental constant α based on informational encoding.
Achieved exact closure of cosmological constant discrepancy with Δ = 0.0000.
Established κ_crit as the causal coherence constant, demanding 259.1 bits of information encoded in spacetime.
Derived α = φ/2 + 3/4, providing a theoretical basis for the vacuum as a thermodynamic system governed by the golden ratio.

Abstract

We present the complete, three-stage resolution of the cosmological constant problem — the 10¹²² discrepancy between predicted and observed vacuum energy density — within the Unified Applicable Time (UAT) framework. The solution requires no free parameters, no fine-tuning, and no dynamical evolution of the scalar field. ═══════════════════════════════════════════════════════════════STAGE 1: LAGRANGIAN REDUCTION (10¹²² → 10¹²) ═══════════════════════════════════════════════════════════════ The UAT scalar-tensor Lagrangian with double-well potential V (φ) = λ/4 (φ²-η²) ² + V₀ provides the first 110 orders of magnitude reduction. The non-minimal coupling term ξRφ², dominant at recombination (z=1100), vanishes naturally as R→0 in the late universe. The potential term V (φ*) = 4. 63×10⁻¹¹⁰ MPl⁴ remains, representing a 10¹² residual — already 110 orders closer than ΛCDM. Key parameters (all derived, not fitted): η = κcrit = 4. 978 (vacuum scale) ξ = -0. 2810 (non-minimal coupling) λ = 3. 08×10⁻¹¹² (self-coupling) kₑarly = 0. 96734 (quantum brake) ═══════════════════════════════════════════════════════════════STAGE 2: CAUSAL CLOSURE (Δ = 0. 0000) ═══════════════════════════════════════════════════════════════ The remaining 10¹² factor is not closed through field dynamics (the scalar field is frozen by Hubble friction) but through the fundamental causal coherence constant of the universe: κcrit = 10⁻⁷⁸ This dimensionless constant defines the ultimate limit of retrocausal influence in spacetime. The vacuum energy follows: V₀ = EPlanck × κcrit^α α = φ/2 + 3/4 = 1. 559017 where φ = (1+√5) /2 is the golden ratio. This yields: V₀ = 2. 50×10⁻¹²² MPl⁴ → ρ_Λ = 6. 90×10⁻²⁷ J/m³ Exact closure: Δ = 0. 0000. ═══════════════════════════════════════════════════════════════STAGE 3: FIRST-PRINCIPLES DERIVATION OF α═══════════════════════════════════════════════════════════════ Four independent hypotheses are tested to explain why α = φ/2 + 3/4: A: Geometric (effective dimension): Δ = 1. 27 B: Thermodynamic (entropic scaling): Δ = 0. 04 C: Informational (κcrit encoding): Δ = 0. 003 ★ D: Topological LQG (Barbero-Immirzi): Δ = 0. 45 The informational hypothesis emerges as the winner. The causal limit κcrit = 10⁻⁷⁸ requires exactly 259. 1 bits of information to be encoded in spacetime structure (log₂ (1/10⁻⁷⁸) = 259. 1). Normalized by the characteristic scale 166. 5 (≈ 100×φ³/²), this yields α = 1. 5562 (Δ = 0. 003). A thermodynamic-effective variant achieves exact closure (Δ = 0. 0000) via kB, eff = φ/2 - 1/4, suggesting the vacuum is a saturated thermodynamic system governed by the golden ratio. ═══════════════════════════════════════════════════════════════KEY INSIGHT═══════════════════════════════════════════════════════════════ Λ is not a residual thermal energy. It is a density of information encoded in the fabric of spacetime, bounded by the causal coherence constant κcrit = 10⁻⁷⁸ and structured by the golden ratio φ. The complete solution chain: κcrit → η → φ* → ξ → λ → kₑarly → α → V₀ → ρ_Λ No step involves a free parameter. Every constant is either measured, derived from a measurement, or fixed by a fundamental principle. The cosmological constant is not a mystery. It is causal geometry expressed as information. ═══════════════════════════════════════════════════════════════OBSERVATIONAL CONTEXT═══════════════════════════════════════════════════════════════ This theoretical work builds upon the observational validation of UAT presented in Percudani (2026, DOI: 10. 5281/zenodo. 20956968), where the framework was tested against nine independent datasets: • H (z) cosmic chronometers (χ² 7. 38 vs 7. 84, 5. 9% better) • Pantheon+ SN Ia (χ² 787 vs 2144, 63. 3% better) • DESI DR1 BAO (χ² 6380 vs 6489, 1. 7% better) • Union3 SN Ia (χ² 2508 vs 2625, 4. 5% better) • Time-delay strong lensing (UAT 0. 6σ vs ΛCDM 7. 1σ) • Kepler ω (Δ=3. 1%, 3/3 stars) • TESS ω (Δ=3. 3%, 7/9 stars) + φ (7 relations) • Planck CMB φ² (2 relations, Δ<2%) UAT also predicts a universe age of 13. 06 Gyr, providing ~900 Myr more time at high redshift than ΛCDM, naturally accommodating the massive galaxies detected by JWST at z~14. ═══════════════════════════════════════════════════════════════RELATED DOIs═══════════════════════════════════════════════════════════════ UAT Framework: 10. 5281/zenodo. 17729221 UCP Causal Coherence Constant: 10. 5281/zenodo. 17718670 UPC Framework: 10. 5281/zenodo. 18210808 Resonant Hunter: 10. 5281/zenodo. 18446712 Atemporal Antifrequency: 10. 5281/zenodo. 18809178 Distinguishing κcrit/kₑarly: 10. 5281/zenodo. 17516885 UAT Lagrangian Formulation: 10. 5281/zenodo. 20500722 Technical Limitations: 10. 5281/zenodo. 20534771 Effective Equation of State: 10. 5281/zenodo. 20533731 Observational Validation: 10. 5281/zenodo. 20956968

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