Confirming the uniformity of the Hubble flow with Pantheon+ Supernovae

TL;DR

This work tests the Cosmological Principle by examining the uniformity of the local Hubble flow through rest-frame differences of $H_0$ across radial shells using the Pantheon+SH0ES Type Ia SN data. Employing a linear Hubble law in shells, the authors compute $\Delta H_s = H_s^{\mathrm{CRF}} - H_s^{\mathrm{LRF}}$ and validate the approach with Monte Carlo realizations to assess isotropy and bias. They find that $\Delta H_s$ tends toward zero for shells with $D_s \gtrsim 85$ Mpc, consistent with ΛCDM predictions and previous CF3-based results, indicating the Hubble flow becomes uniform on scales of $70-100$ Mpc. The results are robust to removing SH0ES data and when using the Hubble-diagram redshift, and future peculiar-velocity surveys will further sharpen these tests. Overall, the Pantheon+SH0ES SN sample provides strong, SN-based support for the CP-driven, statistically uniform Hubble expansion on large scales.

Abstract

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 $ΔH_0 \approx 0$ 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.

Figures (9)

• Figure 1: Mollweide projection showing the sky distribution of Pantheon+SH0ES supernovae: black represents sources with $z < 0.01$, blue corresponds to $0.01 < z < 0.03$, and white denotes $z > 0.03$.
• Figure 2: Difference in the average Hubble constant, $\Delta H_s$, between the CMB and Local Group rest frames for Pantheon+SH0ES and CF3 dataset, shown as a function of shell-averaged distance $D_s$. The values are computed in successive spherical shells of width $\Delta D = 30$ Mpc, with minimum distances of $20$, $30$, and $40$ Mpc. The error bars represent 2$\sigma$ uncertainties. Numerical values are listed in Table 1.
• Figure 3: Comparison of the differential Hubble constant, $\Delta H_s$, between the CMB and LG rest frames based on 1,000 MC realisations. The results from observational data are contrasted with two simulated ensembles: the MC-boost realisations (shaded in light red) and the MC-$\Lambda$CDM realisations (shaded in light blue). The shaded bands represent the median $\Delta H_s$ trend across all realisations, with widths defined by the corresponding median $2\sigma_{\Delta H_s}$ uncertainties.
• Figure 4: Same as Fig. \ref{['fig:simu']}, but showing results for uniformly distributed Monte Carlo realisations.
• Figure 5: Same as Fig. \ref{['fig:simu']}, but for Pantheon+ compilation exclude SH0ES instead.