Revealing the late-time transition of $H_{0}$: relieve the Hubble crisis

The discrepancy between the value of the Hubble constant $H_0$ measured from the local distance ladder and from the cosmic microwave background is the most serious challenge to the standard $\Lambda$CDM model. Various models have been proposed to solve or relieve it, but no satisfactory solution has been given until now. Here, we report a late-time transition of $H_{0}$, i.e., $H_0$ changes from a low value to a high one from early to late cosmic time, by investigating the Hubble parameter $H(z)$ data based on the Gaussian process (GP) method. This finding effectively reduces the Hubble crisis by 70\%. Our results are also consistent with the descending trend of $H_0$ measured using time-delay cosmography of lensed quasars at 1$\sigma$ confidence level, and support the idea that the Hubble crisis arises from new physics beyond the standard $\Lambda$CDM model. In addition, in the $\Lambda$CDM model and $w$CDM model, there is no transition behavior of $H_{0}$.