Redshift Dependence of $H_0$ Dipole in Pantheon+ Supernovae
We examine the dipole structure in the local cosmic expansion rate $H_0$ using the Pantheon+ compilation of Type Ia supernovae. We reconstruct directional maps of $H_0$ across the sky within the low-redshift regime, $z_{\rm min} < z < 0.2$, evaluated in the CMB rest frame. To perform a tomographic analysis, we choose 10 different values for $z_{\rm min}\in [0.015 , 0.045]$ range. We find a dipole amplitude $A_{\rm dip}=1.16\pm0.28\ {\rm km/s/Mpc}$ for the lowest bin, monotonically decreasing to $A_{\rm dip} =0.35\pm0.52\ {\rm km/s/Mpc}$, as we increase $z_{\rm min}$. Since $A_{\rm dip}$ is positive-definite, by construction $A_{\rm dip} > 0$ even in an isotropic universe, thus to assess the statistical significance, we compare to $A_{\rm dip}$ generated from 1000 Monte Carlo simulations based on the $Λ$CDM model and the same redshift ranges. Our results reveal a $2-3σ$ dipole pattern (depending on how the significance level is computed) for $z_{\rm min}\lesssim 0.032$. For redshift thresholds where the signal remains statistically significant ($>2σ$), the inferred dipole direction points close to Shapley supercluster and CMB dipole directions. As $z_{\rm min}$ increases, the dipole amplitude diminishes in line with expectations of a higher redshift isotropic Universe, but the difference in maximal antipodal $H_0$ determinations, $Δ\text{H}_0^{\rm max}$, retain a signal of an anisotropy that disappears in the dipole ansatz. The decreasing statistical significance of all estimators with increasing $z_{\rm min}$ suggests that any $H_0$ dipole is a low-redshift feature.