Potentialities of Hubble parameter and expansion rate function data to
  alleviate Hubble tension
  Taking advantage of Gaussian process (GP), we obtain an improved estimate of
the Hubble constant, $H_0=70.41\pm1.58$ km s$^{-1}$ Mpc$^{-1}$, using Hubble
parameter [$H(z)$] from cosmic chronometers (CCH) and expansion rate function
[$E(z)$], extracted from type Ia supernovae, data. This result is higher than
those obtained by directly reconstructing CCH data with GP. In order to
estimate the potential of future CCH data, we simulate two sets of $H(z)$ data
and use them to constrain $H_0$ by either using GP reconstruction or fitting
them with $E(z)$ data. We find that simulated $H(z)$ data alleviate $H_0$
tension by pushing $H_0$ values higher towards $\sim70$ km s$^{-1}$ Mpc$^{-1}$.
We also find that joint $H(z)$ + $E(z)$ data favor higher values of $H_0$,
which is also confirmed by constraining $H_0$ in the flat concordance model and
2-order Taylor expansion of $H(z)$. In summary, we conclude that more and
better-quality CCH data as well as $E(z)$ data can provide a new and useful
perspective on resolving $H_0$ tension.
