No-go guide for late-time solutions to the Hubble tension: Matter perturbations

The Hubble tension seems to be a crisis with $\sim5\sigma$ discrepancy between the most recent local distance ladder measurement from type Ia supernovae calibrated by Cepheids and global fitting constraint cosmic microwave background data. To narrow down possible late-time solutions tension, we have used in study [Phys. Rev. D 105, L021301 (2022)] an improved inverse method absolute measurements of expansion rate at high redshifts chronometer data, found no appealing evidence for new physics late time beyond $\Lambda$CDM model characterized parametrization based on age. In this paper, further investigate perspective including matter perturbation growth Independent dataset choices, parametrizations, diagnostic quantities ($S_8$ $S_{12}$), is strongly disfavored so that previous no-go guide strengthened.