Pantheon+ tomography and Hubble tension

The recently released Type Ia supernovae (SNe Ia) sample, Pantheon+, is an updated version of Pantheon and has very important cosmological implications. To explore the origin of the enhanced constraining power and internal correlations of datasets in different redshifts, we perform a comprehensively tomographic analysis of the Pantheon+ sample without and with the Cepheid host distance calibration, respectively. Specifically, we take two binning methods to analyze the Pantheon+ sample, i.e., equal redshift interval and equal supernovae number for each bin. For the case of equal redshift interval, after dividing the sample to 10 bins, the first bin in the redshift range $z\in[0.00122, \, 0.227235]$ dominates the constraining power of the whole sample. For the case of equal supernovae number, the first three low redshift bins prefer a large matter fraction $\Omega_m$ and only the sixth bin gives a relatively low cosmic expansion rate $H_0$. For both binning methods, we find no obvious evidence of evolution of $H_0$ and $\Omega_m$ at the $2\,\sigma$ confidence level. The inclusion of the SH0ES calibration can significantly compress the parameter space of background dynamics of the universe in each bin. When not considering the calibration, combining the Pantheon+ sample with cosmic microwave background, baryon acoustic oscillations, cosmic chronometers, galaxy clustering and weak lensing data, we give the strongest $1\,\sigma$ constraint $H_0=67.88\pm0.42$ km s$^{-1}$ Mpc$^{-1}$. However, the addition of the calibration leads to a global shift of the parameter space from the combined constraint and $H_0=68.66\pm0.42$ km s$^{-1}$ Mpc$^{-1}$, which is inconsistent with the Planck-2018 result at about $2\,\sigma$ confidence level.