Confirming the uniformity of the Hubble flow with Pantheon+ Supernovae

According to the perturbed Friedmann model, the difference between Hubble constant measurements in two rest frames, at leading order in velocity, is determined solely by the relative motion of the observers and remains unaffected by the peculiar velocities of the sources. This implies that, when averaging over a sufficiently large and distant set of sources where local nonlinear inhomogeneities are diminished, such a difference should vanish, so that the Hubble flow is statistically uniform, as predicted by the Cosmological Principle -- a core assumption of the standard cosmological paradigm. In previous works, distance measurement compilations, e.g. the CosmicFlows-3 catalogue, were used for this purpose, as it comprises a large number ($\sim 10^4$) of sources of different types. Due to the increasing amount of precise luminosity distance measurements of Type Ia Supenovae (SNe) in the last few years, in this work we investigate whether we can confirm the uniformity of the Hubble flow with low-$z$ SN distances only. By means of the Pantheon+ and SH0ES compilation, we find that the results align well with previous works based on the CF3 catalogue, and are in good agreement with the expected Hubble variance in the standard model across cosmic scales of $20-150$ Mpc. Notably, the Hubble constant difference $\Delta H_0 \approx 0$ is observed at around $85$ Mpc. Despite the smaller sample size ($\sim 10^2$ versus $\sim 10^4$) relative to CF3 at those scales, our analysis show that the Pantheon+ and SH0ES dataset supports the standard model paradigm, which indicates that the Hubble flow becomes statistically uniform at around $70-100$ Mpc, which is compatible with independent determinations of the homogeneity scale based on galaxy number counts.