Distance Ladder Coherence

ΛCDM is built on the assumption that the universe is homogeneous and isotropic on large scales, which implies the Hubble flow should be smooth and predictable once one averages over sufficiently large volumes. The distance ladder measures this flow by stacking Cepheids, TRGB stars, and SBF to calibrate Type Ia supernovae, which then probe H₀ in the linear Hubble flow regime beyond ~100 Mpc. "Coherence" refers to the internal consistency of this chain: whether each rung agrees with the next, whether the supernovae used to derive H₀ span a representative cosmic volume, and whether peculiar velocities have been adequately accounted for. Detailed analyses reveal that the inferred H₀ shows a mild but statistically meaningful trend with the distance of the supernova sample — nearer samples yield slightly higher H₀, and the value stabilizes only beyond ~150 Mpc.

This gradient hints that the local universe — out to a few hundred megaparsecs — may have a slightly higher expansion rate than the cosmic mean, possibly because we reside in or near a large underdensity (a "local void"). ΛCDM does predict some variance in locally measured H₀ due to large-scale structure, but the predicted cosmic variance is typically only 0.5–1 km/s/Mpc, far smaller than the observed ~5–6 km/s/Mpc discrepancy with Planck. A local void large enough to explain the full Hubble tension would be in significant tension with the ΛCDM matter power spectrum, which places tight constraints on how deep and wide such voids can be. The coherence analysis thus transforms the Hubble tension from a calibration problem into a potential structural feature of the local universe that ΛCDM struggles to accommodate.