Growth of Cosmic Structure in the UAT Framework: Bayesian Model Selection, Parameter Sweep, and the Decisive Preference for Predictive Rigidity over Parametric Freedom

TECHNICAL NOTE — ZENODO DEPOSIT (UPDATE) Author: Miguel Ángel PercudaniORCID: 0009-0007-1748-3212 ═══════════════════════════════════════════════════════════════ABSTRACT═══════════════════════════════════════════════════════════════ This note presents a complete statistical evaluation of the Unified Applicable Time (UAT) framework against 26 published measurements of the linear growth rate fσ₈ (z). The analysis comprises three components: 1. FIRST-ORDER GROWTH RATE CALCULATION: The growth equation is solved using the UAT-modified H (z) with the quantum brake parameter kₑarly = 0. 96734 (derived from the single free parameter of the theory: the 7% thermal calibration margin). χ² (UAT) = 17. 28 (χ²/dof = 0. 69) χ² (ΛCDM) = 15. 93 (χ²/dof = 0. 80) Δχ² = 1. 35 (~1. 2σ) 2. PARAMETER SWEEP: • kₑarly sweep with fσ₈ (z): Canonical value 0. 96734 lies at the edge of the 68% CL interval 0. 9761, 1. 0000. Δχ² = 1. 36. • κcrit sweep with Λ: Canonical value 10⁻⁷⁸ predicts Λ = 2. 49×10⁻¹²² vs observed 2. 47×10⁻¹²² MPl⁴ (~0. 8% deviation). 3. BAYESIAN MODEL SELECTION (key result): • AIC: UAT = 19. 28, ΛCDM = 27. 93. ΔAIC = -8. 65. UAT weight = 98. 7% • BIC: UAT = 20. 54, ΛCDM = 35. 48. ΔBIC = -14. 94. UAT weight = 99. 9% • Bayes Factor (Schwarz): B ≈ 1755 in favor of UAT. Jeffreys scale: B > 100 = "DECISIVE evidence" Sensitivity analysis: ΛCDM would need to reduce its free parameters from 6 to ~1. 4 for the Bayes factor to be neutral. CONCLUSION: A model with a single, physically-motivated free parameter (the 7% thermal calibration margin, constrained by the existence of cosmic structures) achieves a fit that is FORMALLY AND DECISIVELY PREFERRED over the fully calibrated standard model with six or more parameters. The raw χ² difference (Δχ² = 1. 35) is overwhelmed by the penalty for parametric complexity when proper model selection criteria are applied. This is not merely a demonstration that UAT is "competitive" with ΛCDM. It is a formal Bayesian demonstration that UAT is decisively preferred for this observable. LIMITATIONS (explicitly acknowledged): • First-order only: uses only modified H (z). Complete calculation requires a dedicated Boltzmann solver (see DOI: 10. 5281/zenodo. 21317943). • The 7% margin is empirically constrained, not derived from first principles (see DOI: 10. 5281/zenodo. 21211964). • Observational data were calibrated under the ΛCDM assumption. ═══════════════════════════════════════════════════════════════CONTENTS═══════════════════════════════════════════════════════════════ • uatgrowthbayesian. pdf — Complete manuscript • uatgrowthbayesian. tex — LaTeX source • uatₚarameterₛweep. py — kₑarly and κcrit parameter sweeps • uatbayesianₛelection. py — AIC, BIC, Bayes Factor computation ═══════════════════════════════════════════════════════════════REFERENCES═══════════════════════════════════════════════════════════════ UAT Framework: DOI: 10. 5281/zenodo. 17729221UCP Constant κcrit: DOI: 10. 5281/zenodo. 18210808Λ First-Principles Resolution: DOI: 10. 5281/zenodo. 21109424UAT/UCP Synthesis: DOI: 10. 5281/zenodo. 213134687% Thermal Calibration Margin: DOI: 10. 5281/zenodo. 21211964Causal Membrane Dynamics: DOI: 10. 5281/zenodo. 21283136Methodological Limitations: DOI: 10. 5281/zenodo. 21317943 ═══════════════════════════════════════════════════════════════KEYWORDS═══════════════════════════════════════════════════════════════ cosmological constant, dark energy, structure formation, growth rate, fσ8, linear perturbations, causal coherence, Ivancho Limit, quantum brake, Bayesian model selection, Akaike Information Criterion, Bayes Factor, Occam's razor, predictive rigidity, UAT framework, ΛCDM, modified gravity ═══════════════════════════════════════════════════════════════LICENSE═══════════════════════════════════════════════════════════════ Creative Commons Attribution 4. 0 International (CC BY 4. 0)