On the Hubble Constant Tension in the SNe Ia Pantheon Sample

The Hubble constant (H ₀) tension between Type Ia supernovae (SNe Ia) and Planck measurements ranges from 4 to 6σ. To investigate this tension, we estimate H ₀ in the ΛCDM and $w_0{w}_a$CDM (cold dark matter) models by dividing the Pantheon sample, the largest compilation of SNe Ia, into 3, 4, 20, and 40 bins. We fit the extracted H ₀ values with a function mimicking the redshift evolution: $g{\left(z\right)=H_0\left(z\right)={\tilde{H}}_0/(1+z)}^{\alpha }$, where α indicates an evolutionary parameter and ${\tilde{H}}_0=H_0$ at z = 0. We set the absolute magnitude of SNe Ia so that $H_0=73.5km{s}^{-1}{Mpc}^{-1}$, and we fix fiducial values for ${\Omega }_{0m}^{\Lambda CDM}=0.298$ and ${\Omega }_{0m}^{w_0{w}_{a}CDM}=0.308$. We find that H ₀ evolves with redshift, showing a slowly decreasing trend, with α coefficients consistent with zero only from 1.2 to 2.0σ. Although the α coefficients are compatible with zero in 3σ, this however may affect cosmological results. We measure locally a variation of $H_0(z=0)-H_0(z=1)=0.4km{s}^{-1}{Mpc}^{-1}$ in three and four bins. Extrapolating $H_0\left(z\right)$ to z = 1100, the redshift of the last scattering surface, we obtain values of H ₀ compatible in 1σ with Planck measurements independent of the cosmological models and number of bins we investigated. Thus, we have reduced the H ₀ tension in the range from 54% to 72% for both cosmological models. If the decreasing trend of $H_0\left(z\right)$ is real, it could be due to astrophysical selection effects or to modified gravity.