Revealing the late-time transition of $H_{0}$: relieve the Hubble crisis
  The discrepancy between the value of the Hubble constant $H_0$ measured using
the local distance ladder and the value inferred using the cosmic microwave
background is the most serious challenge to the standard $\Lambda$CDM model.
Many models have been suggested to solve or relieve it. Here, we report a
late-time transition of $H_{0}$, i.e., $H_0$ changes from low value to high one
from early to late cosmic time, by investigating the Hubble parameter $H(z)$
data based on the Gaussian process method. This finding effectively reduces the
Hubble crisis by 70\%. Our results are also consistent with the descending
trend of $H_0$ measured by time-delay cosmography of lensed quasars at
1$\sigma$ confidence level. It is interesting that under the $\Lambda$CDM model
and $w$CDM model, this transition disappears, leaving a bump in redshift range
(0.4, 0.5). This demonstrates the model-independent method should be used to
derive $H_0$.
