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 ($H_0$) 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 paper, 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 $\mathrm{\Lambda }$-cold-dark-matter ($\mathrm{\Lambda }$CDM) 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 $H_0$ tension and $M_B$ tension are absent in our local Universe, a combination of $H_0$ and $M_B$ as the intercept $a_B$ of the magnitude-redshift relation exhibits $3\sim 7\sigma$ tension even for the $\mathrm{\Lambda }$CDM model. This $a_B$ tension seems to call for local-scale inhomogeneous new physics disguised as local observational systematics.