Evidence for a Positive Correlation between H0 and Baryonic Overdensity across 36 Independent Measurements

The persistent∼5σ discrepancy between locally measured (H0 ≃73 km/s/Mpc) and CMB-inferred (H0 ≃

67.4 km/s/Mpc) values of the Hubble constant has motivated both systematic re-examinations and proposals for new physics. An alternative possibility, less thoroughly explored, is that measurements probing different large-scale baryonic environments sample an intrinsic environmental gradient in the apparent expansion rate. We compile 36 published H0 measurements from 16 independent methodological categories (X-ray clusters, SN Ia, SN II, Cepheids, TRGB, JAGB, Miras, CMB, BAO, Tully–Fisher, strong lensing, gravitational waves, SBF, maser, H II regions, cosmic chronometers) and assign each a baryonic overdensity δb along the line of sight, reconstructed from the 2M++ density catalog (Lavaux & Hudson 2011) for the 15 highest-quality (Tier A) measurements, and from environmental literature estimates for the remaining 21. We perform a weighted least-squares regression and six independent statistical tests.
We report a positive linear correlation:

H0 = (67.44 ±0.36) + (1.45 ±0.20) ×δb [km/s/Mpc]

at a formal significance of 7.3σ (χ2 = 9.9, ν = 34). We note that χ2/ν = 0.29, indicating that stated measurement uncertainties are likely conservative for this compilation; however, the non-parametric permutation test (p= 7.3 ×10−6) and bootstrap (95 % CI: [1.14, 1.63]), which are independent of the error magnitudes, confirm the signal. The intercept matches the Planck CMB value at 0.1σ . The correlation persists across all subset removals (minimum 4.0σ for the 15 Tier A measurements alone, where δb is reconstructed independently of H0) and no individual data point is influential. The observed slope is opposite in sign to a simple linear ΛCDM prediction, though rigorous N-body quantification remains outstanding. If this correlation is confirmed by future directional measurements and simulations, it would suggest that at least part of the H0 discrepancy reflects a dependence of the apparent expansion rate on the baryonic environment, rather than a single global systematic or new-physics effect alone. Our analysis is purely empirical; we do not propose a causal mechanism, and we caution that the heterogeneous nature of the δb assignments for Tiers B and C represents the primary limitation of the present work.