Phenomenological Measurement of Omega_m h^2 and H_0 from DESI DR2, Pantheon+, and CMB Shift Data

Abstract

Phenomenological Measurement of Omega_m h^2 and H_0 from DESI DR2, Pantheon+, and CMB Shift Data Authors: Miguel Ángel Percudani (ORCID: 0009-0007-1748-3212), Jorge Iván Díaz Repository DOI: 10.5281/zenodo.22853862 --- DESCRIPTION This repository contains a fully reproducible MCMC analysis of the cosmological parameters H_0 and Omega_m h^2 using three independent datasets: - DESI DR2 baryon acoustic oscillation (BAO) measurements (13 data points, full covariance)- Pantheon+ Type Ia supernovae (1590 SNe with z > 0.01, full statistical + systematic covariance)- CMB shift parameters (l_A and R from Planck 2018) The analysis assumes a spatially flat LambdaCDM background. No extended framework is assumed or tested. The goal is a phenomenological measurement of standard cosmological parameters, compared with the Planck 2018 determination. RESULTS H_0 = 69.91 ± 0.71 km/s/MpcOmega_m h^2 = 0.14763 ± 0.00126chi^2_best = 1420.53 (for N = 1605 data points, reduced chi^2 ≈ 0.885)Effective sample sizes: ESS(H_0) ≈ 2385, ESS(Omega_m h^2) ≈ 2396 The measured value of Omega_m h^2 is 3.8% higher than the Planck 2018 value (0.14222 ± 0.00083) at approximately 3.6 sigma. This deviation connects to the well-documented tension between early-universe probes (CMB) and late-universe probes (BAO + SNe Ia). It is not interpreted here as evidence for any extension beyond LambdaCDM; it is a measurement of the matter density using three independent datasets. The H_0 value obtained here (69.91 ± 0.71) lies between the Planck value (67.4) and the SH0ES value (73.0), consistent with other combined analyses. STABILITY TEST To verify that results do not depend on the random seed initialization, four independent MCMC runs were performed with different seeds (42, 123, 2024, 7). All runs converge to the same best-fit chi^2 value and produce parameter values within 1 sigma of the baseline. The scatter across seeds is 69x (H_0) and 80x (Omega_m h^2) smaller than the individual parameter uncertainties, confirming both convergence and reproducibility. Weighted mean across seeds: H_0 = 69.928 ± 0.361 km/s/Mpc, Omega_m h^2 = 0.14765 ± 0.00064. REPOSITORY CONTENTS - cosmo_measurement.py — main analysis script (downloads data, runs MCMC, generates figures, packages results)- stability_test.py — multi-seed stability verification- results.json — summary statistics (parameters, chi^2, ESS, stability test)- stability_summary.json — detailed stability test output- chain_full.npy, chain_flat.npy, logp_full.npy, logp_flat.npy — baseline MCMC chain (seed 42)- chain_seed42.npy, chain_seed123.npy, chain_seed2024.npy, chain_seed7.npy — stability test chains- data/ — DESI DR2 BAO, Pantheon+ SNe, and CMB shift input files- figures/ — MCMC traces, corner plot, stability test plot- README.md — full reproduction instructions- UAT_k978_report.pdf — compiled LaTeX paper with all results METHOD Flat LambdaCDM model: E^2(z) = Omega_m (1+z)^3 + Omega_r (1+z)^4 + Omega_Lambda, with Omega_r fixed to 9.15e-5.Free parameters: H_0 and Omega_m h^2.Likelihood: -2 ln L = chi^2_SN + chi^2_BAO + chi^2_CMB.MCMC sampler: emcee with 32 walkers, 2500 steps, 700 burn-in.Priors: 55 < H_0 < 85 km/s/Mpc, 0.10 < Omega_m h^2 < 0.20. REPRODUCIBILITY The analysis is fully deterministic. Repeated runs with the same random seed produce identical chains. All data files are downloaded automatically from public GitHub repositories (CobayaSampler, PantheonPlusSH0ES). The pipeline runs in approximately 19 minutes on a Google Colab T4 instance. RELATED WORK This measurement is consistent in direction and magnitude with recent independent analyses of DESI DR2 data:- Chaudhary et al. (2025) report a 1.84 sigma tension in Omega_m between low and high redshift DESI DR2 bins.- Jia et al. (2025) find H_0 = 69.29 ± 0.81 km/s/Mpc using Gaussian process regression on DESI DR2 + Pantheon+.- Farren et al. (2025) report tensions of 1.6-3.7 sigma in the Omega_m - H_0 r_d plane when combining DESI BAO, CMB, and SNe Ia. CITATION Percudani, M. A., & Díaz, J. I. (2026). Phenomenological Measurement of Omega_m h^2 and H_0 from DESI DR2, Pantheon+, and CMB Shift Data. Zenodo. https://doi.org/10.5281/zenodo.22853862 CONTACT Miguel Ángel Percudani — miguel_percudani@yahoo.com.ar — ORCID: 0009-0007-1748-3212 LICENSE CC BY 4.0