The tension on the cosmological parameters from different observational data

Abstract: Planck measurements of the cosmic microwave background power spectra find a lower value of the Hubble constant $H_0$ and a higher value of the fractional matter energy density $\Omega_{m0}$ for the concordance $\Lambda$CDM model, and these results are in tension with other measurements. The {\em Planck} group argued that the tension came either from some sources of unknown systematic errors in some astrophysical measurements or the wrong $\Lambda$CDM model applied in fitting the data. We studied the reason for the tension on $H_0$ from different measurements by considering two dynamical dark energy models. We found that there is no tension between different data, the constraint on $H_0$ is almost unchanged for different dark energy models and the tension with the local measurements remains when the error bar on $H_0$ is tightened to be around 1. We argue that the tension on $H_0$ is not caused by the fitting model.