A reanalysis of the latest SH0ES data for $H_0$: Effects of new degrees of freedom on the Hubble tension

We reanalyze the recently released SH0ES data for the determination of $H_0$. We focus on testing the homogeneity of the Cepheid+SnIa sample and the robustness of the results in the presence of new degrees of freedom in the modeling of Cepheids and SnIa. We thus focus on the four modeling parameters of the analysis: the fiducial luminosity of SnIa $M_B$ and Cepheids $M_W$ and the two parameters ($b_W$ and $Z_W$) standardizing Cepheid luminosities with period and metallicity. After reproducing the SH0ES baseline model results, we allow for a transition of the value of any one of these parameters at a given distance $D_c$ or cosmic time $t_c$ thus adding a single degree of freedom in the analysis. When the SnIa absolute magnitude $M_B$ is allowed to have a transition at $D_c\simeq 50Mpc$ (about $160Myrs$ ago), the best fit value of the Hubble parameter drops from $H_{0}=73.04\pm1.04\,km\,s^{-1}\,Mpc^{-1}$ to $H_0=67.32\pm 4.64\, km\,s^{-1}\,Mpc^{-1}$ in full consistency with the Planck value. Also, the best fit SnIa absolute magnitude $M_B^>$ for $D>D_c$ drops to the Planck inverse distance ladder value $M_{B}^>=-19.43\pm 0.15$ while the low distance best fit $M_B^<$ parameter remains close to the original distance ladder calibrated value $M_{B}^<=-19.25\pm 0.03$. Similar hints for a transition behavior is found for the other three main parameters of the analysis ($b_W$, $M_W$ and $Z_W$) at the same critical distance $D_c\simeq 50\,Mpc$ even though in that case the best fit value of $H_0$ is not significantly affected. When the inverse distance ladder constraint on $M_B^>$ is included in the analysis, the uncertainties for $H_0$ reduce dramatically ($H_0= 68.2\pm 0.8\, km\,s^{-1}\,Mpc^{-1}$) and the $M_B$ transition model is strongly preferred over the baseline SH0ES model ($\Delta \chi^2 \simeq -15$, $\Delta AIC \simeq -13$) according to AIC and BIC model selection criteria.