Exploratory Laboratory: The UAT Framework and the Hubble Tension — MCMC Analyses with Pantheon+, Planck, and BOSS Data

This repository contains an exploratory and speculative investigation of the Unified Applicable Time (UAT) framework, a phenomenological cosmological model that introduces a quantum-braking parameter (kₑarly) to modify the early-universe expansion history. What is in this repository? A comprehensive laboratory report (PDF, LaTeX source) describing nine MCMC phases of increasing complexity. Python scripts for all phases, from synthetic data tests to the final hardcore analysis (Phase 9) with 5000 MCMC steps, full Pantheon+ covariance matrix, and convergence diagnostics. Posterior corner plots and goodness-of-fit tables. The dialogue between the author and the AI assistant DeepSeek that guided the analysis. Data used: Pantheon+ Type Ia supernovae (1587 SNe, full statistical+systematic covariance matrix). Planck 2018 CMB shift parameter (R = 1. 7496 ± 0. 0094). BOSS DR12 BAO measurements (DM/rd and DH/rd) and cosmic chronometers H (z). SH0ES prior on H0 (73. 04 ± 1. 0 km/s/Mpc). Key result: Under the stress of a high local H0 prior, the UAT model consistently prefers kₑarly < 1, with a final median of kₑarly = 0. 982 (only ~1. 5% away from the theoretically motivated value of 0. 967). The fit to CMB and BAO data improves slightly compared to ΛCDM, although the total χ² is practically identical. Important caveat: This work is a curiosity-driven intellectual exercise. It does not constitute a formal validation of new physics, nor has it been peer-reviewed. The UAT framework remains speculative and lacks a full Lagrangian formulation. All results should be interpreted as exploratory and provisional. Author: Miguel Ángel Percudani (Puan, Buenos Aires, Argentina) Contact: miguelₚercudani@yahoo. com. ar License: Creative Commons Attribution 4. 0 International (CC BY 4. 0)