Redshift Dependence of $H_0$ Dipole in Pantheon+ Supernovae

Abstract

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, $z_{\min }<z<0.2$, evaluated in the CMB rest frame. To perform a tomographic analysis, we choose 10 different values for $z_{\min }\in [0.015,0.045]$ range. We find a dipole amplitude $A_{\mathrm{dip}}=1.16\pm 0.28km/s/Mpc$ for the lowest bin, monotonically decreasing to $A_{\mathrm{dip}}=0.35\pm 0.52km/s/Mpc$, as we increase $z_{\min }$. Since $A_{\mathrm{dip}}$ is positive-definite, by construction $A_{\mathrm{dip}}>0$ even in an isotropic universe, thus to assess the statistical significance, we compare to $A_{\mathrm{dip}}$ generated from 1000 Monte Carlo simulations based on the $\Lambda$CDM model and the same redshift ranges. Our results reveal a $2-3\sigma$ dipole pattern (depending on how the significance level is computed) for $z_{\min }\lesssim 0.032$. For redshift thresholds where the signal remains statistically significant ($>2\sigma$), the inferred dipole direction points close to Shapley supercluster and CMB dipole directions. As $z_{\min }$ increases, the dipole amplitude diminishes in line with expectations of a higher redshift isotropic Universe, but the difference in maximal antipodal $H_0$ determinations, $\Delta {\text{H}}_0^{\max }$, retain a signal of an anisotropy that disappears in the dipole ansatz. The decreasing statistical significance of all estimators with increasing $z_{\min }$ suggests that any $H_0$ dipole is a low-redshift feature.

17pages, 8 Figures, 3 Tables