No-go guide for the Hubble tension: Late-time or local-scale new physics

The standard model of modern cosmology might be cracked by the recent persistent hot debate on the Hubble-constant (H₀) tension, which manifests itself as the sound-horizon (r_s) tension or absolute-magnitude (M_B) tension if deeming the origin of the Hubble tension from modifying the early or late Universe, respectively. In this study, we achieve a fully model-independent constraint (fitting a model-independent global parameterization to a model-independent inverse distant ladder with a model-independent high-redshift calibration) on late-time models with strong evidence against homogeneous new physics over the Λ-cold-dark-matter (ΛCDM) model. Further using this model-independent constraint to calibrate sufficiently local supernovae with corresponding late-time models extrapolated below the homogeneity scale, we find surprisingly that, although both H₀ tension and M_B tension are absent in our local Universe, a combination of H₀ and M_B as the intercept a_B of the magnitude-redshift relation exhibits 3 ∼ 7σ tension even for the ΛCDM model. This a_B tension seems to call for local-scale inhomogeneous new physics disguised as local observational systematics.