Towards to $H_0$ Tension by the Theoretical Hubble Parameter in the Infinite Future.

There exists a constant value of $H(z)$ at $z=-1$ when in $\omega$CDM universe with $\omega > -1$, which is independent on other cosmological parameters. We first combine this theoretical $H(z)$ value with the latest 43 observational $H(z)$ data (OHD) to perform the model-independent Gaussian Processes (GP) and constrain the Hubble constant. We obtain $H_0$=67.67$\pm3.03\ {\rm km\ s^{-1} Mpc^{-1}}$, which is in agreement with $H_0$ values from Plank Collaboration (2015) ($0.24 \sigma $ tension) but a larger deviation from Riess et al. (2016) ($1.60 \sigma $ tension), while $H_0$=71.09\ $\pm3.71\ {\rm km\ s^{-1} Mpc^{-1}}$ $ (0.64 \sigma $ tension) by only using latest 43 OHD. Using this $H_0$ value, we perform $\chi^2$ statistics with Markov Chain Monte Carlo (MCMC) method to constrain cosmological parameters. We obtain $\Omega_M=0.26 \pm 0.02$ and $\omega=-0.85 \pm 0.06$ in flat $\omega CDM$ model, and $\Omega_M=0.27\pm 0.04 , \Omega_\Lambda=0.80 \pm 0.12$ and $\omega=-0.82 \pm 0.07$ in non-flat $\omega CDM$ model, which are larger than those not using the theoretical $H(z)$ value.