Complete Resolution of the Cosmological Constant Problem: Zero-Parameter Derivation from the Two-State Intertwiner Boltzmann Mechanism via the Koszul Bridge (Paper 37 in the Intertwiner Series)
Year: 2026
Type: preprint
Abstract: We show that the cosmological constant problem is resolved by recognizing that the gravitational vacuum energy is determined by the two-state intertwiner Hilbert space H_int = span{|k=0⟩, |k=1⟩} of the four-valent vertex in loop quantum gravity, rather than by the infinitely many zero-point modes of quantum field theory. We prove three results that close the logical chain from the LQG vertex to the observed value of Λ: (1) a spectral action uniqueness theorem showing that the second spectral moment M₂ = 240 is the unique gravitational spectral action satisfying endogeneity, spectral locality, parity, non-perturbative completeness, and gravitational correspondence on the reflectionless bounce geometry — higher curvature corrections are excluded by the zero-radius-of-convergence and non-Borel-summability of the Connes–Chamseddine heat-kernel series; (2) a proposition chain deriving the Boltzmann vacuum energy ρ_Λ = ρ_P e^{−V₄} from the KMS state, with the energy scale ρ_{k=1} = ρ_P derived from Casimir coupling; (3) an exponential channeling theorem proving that Standard Model vacuum shifts enter the exponent via Casimir asymmetry (C₀ = 0, C₁ = 2), not as additive corrections. The Boltzmann probability of the k = 1 intertwiner state, with Euclidean action V₄ = 280 derived from three spectral invariants {M₀ = 12, M₂ = 240, κ₀² = 2} of the loop quantum cosmology bounce window function, gives ρ_Λ/ρ_P = e^{−280} ≈ 10^{−122}, matching the Planck 2018 observed value to 0.8%. The exponential structure automatically protects the hierarchy: electroweak and QCD vacuum shifts enter the exponent as corrections of order 10^{−67}, converting the standard 10^{54} fine-tuning catastrophe into a negligible multiplicative factor. As of Paper 47 of this series, four of the five spectral inputs (κ₀² = 2, λ = 1, M₀ = 12, and the bare/dressed rule V₄ = M₂(1 + Σ)) are proved from the recognition cascade via the Koszul bridge; M₂ = 240 follows from the derived κ₀² and the tangent numbers (mathematical constants). The derivation has zero free parameters. We further resolve the QFT vacuum energy discrepancy (the 10^{122} ratio is e^{V₄}, not a fine-tuning) and prove radiative stability from PT reflectionlessness, Koszul nilpotency, and bounce-epoch confinement. Two independent predictions emerge from the same three spectral numbers: the scalar power spectrum amplitude A_s ≈ 2.100 × 10^{−9} (matching Planck to 0.03σ) and the testable identity Λ = A_s^{14}/C_mod.
Author: hillard, shane
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204129108
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