Global Likelihood Analysis of the U-Cell Model: Simultaneous BAO+CC Fit and Comparison with ΛCDM

We present a simultaneous two-dimensional global likelihood analysis of the U-Cell Model (UCM) and ΛCDM over the parameter space (H₀, Ω_m), combining DESI DR2 BAO, eBOSS DR16 BAO, and Cosmic Chronometer (CC) likelihoods (N = 61 data points). This directly addresses the methodological concern that per-probe BIC summation may overlook cross-dataset correlations. The UCM fixes Ω_m = 0.3166 algebraically (zero free cosmological parameters); ΛCDM treats Ω_m as a free parameter. The global fit yields three main results: (1) The UCM joint constraint on the Hubble constant is H₀ = 67.6 ± 0.3 km/s/Mpc, consistent with Planck at 0.9σ. The UCM confirms the CMB-derived value and does not resolve the Hubble tension — which is an observational discrepancy distinct from the theoretical cosmological constant problem the UCM addresses. (2) The BAO+CC global ΔBIC = −2.25 (inconclusive on the Jeffreys scale; threshold > 2), meaning BAO+CC data alone do not significantly distinguish UCM from ΛCDM. The decisive evidence in Paper 28 (ΣΔBIC = +27.1) comes from the supernova sector (three independent compilations, ΔBIC = +18.3 combined), which is unaffected by BAO-CC correlations. (3) The Cosmic Chronometers alone prefer Ω_m = 0.320 ± 0.020 (Paper 17), consistent with UCM at 0.2σ. The 2.6σ BAO+CC tension with Ω_m = 0.3166 is driven by DESI DR2 and eBOSS DR16, which prefer lower Ω_m independently of the UCM — a probe-internal tension also present in DESI DR2 vs. Planck ΛCDM. The analysis code (ucm_global_fit.py) and Cobaya configuration files are included for full reproducibility. Part of the UCM preprint series (ORCID 0009-0005-5088-4339, records 19387201–19413958).