No evidence for local $H_0$ anisotropy from Tully--Fisher or supernova distances

TL;DR

This paper investigates claims of local anisotropy in the Hubble constant using low-redshift distance tracers (Tully–Fisher galaxies and Type Ia supernovae) with $z\lesssim0.05$. It introduces a forward-modeling framework that jointly calibrates distance indicators, marginalizes over distances, and accounts for peculiar velocities via the Carrick_2015 reconstruction, enabling a dipole test in the zero-point or SN absolute magnitude. Analyses of CF4 TFR W1, 2MTF, SFI++, Pantheon+, and Pantheon+ Lane find a significant zero-point dipole in CF4 and Pantheon+ datasets, but allowing a radially varying velocity dipole yields a bulk flow that grows and then decays, consistent with LCDM rather than a true linear $H_0$ anisotropy. The work highlights degeneracies between a cosmological dipole and local flows, demonstrates the necessity of robust forward modeling, and suggests that higher-redshift data is essential to decisively test the CP in the local universe.

Abstract

Claims of local ($z \lesssim 0.05$) anisotropy in the Hubble constant have been made based on direct distance tracers such as Tully-Fisher galaxies and Type Ia supernovae. We revisit these using the CosmicFlows-4 Tully-Fisher W1 subsample, 2MTF and SFI++ Tully-Fisher catalogues, and the Pantheon+ supernova compilation (all restricted to $z < 0.05$), including a dipole in either the Tully-Fisher zero-point or the standardised supernova absolute magnitude. Our forward-modelling framework jointly calibrates the distance relation, marginalises over distances, and accounts for peculiar velocities using a linear-theory reconstruction. We compare the anisotropic and isotropic model using the Bayesian evidence. In the CosmicFlows-4 sample, we infer a zero-point dipole of amplitude $0.087 \pm 0.019$ mag, or $4.1\pm0.9$ per cent when expressed as a dipole in the Hubble parameter. This is consistent with previous estimates but at higher significance: model comparison yields odds of $877:1$ in favour of including the zero-point dipole. In Pantheon+ we infer zero-point dipole amplitude of $0.049 \pm 0.013$ mag, or $2.3\pm 0.6$ per cent when expressed as a dipole in the Hubble parameter. However, by allowing for a radially varying velocity dipole, we show that the anisotropic zero-point model captures local flow features (or possibly systematics) in the data rather than an actual linearly growing effective bulk flow caused by anisotropy in the zero-point or expansion rate. Crucially, inferring a more general bulk flow curve we find results fully consistent with expectations from the standard cosmological model.

Figures (9)

• Figure 1: Comparison of the redshift distribution of the CF4 TFR W1 sample with a mock catalogue generated using the parameters in \ref{['tab:mock_TFR_injected_values']}. The mock is designed to replicate the CF4 subsample and assess how the dipole detection significance depends on sample size.
• Figure 2: Comparison of the inferred TFR zero-point dipole under different Galactic dust corrections using the CF4 TFR W1 data: (a) fixed extinction from the CF4 catalogue which is based on Schlegel_1998, (b) $E(B\!-\!V)$ from Schlegel_1998 with a sampled extinction coefficient $R_{\rm W1}$, (c) $E(B\!-\!V)$ from the Chiang_2023 map, and (d) $E(B\!-\!V)$ from the Planck_2016 map, both also with sampled $R_{\rm W1}$. The recovered zero-point dipole is unaffected by the extinction treatment and its magnitude is $\Delta_{\rm ZP} = 0.087 \pm 0.19$ mag. The values of redshift scatter $\sigma_v$ and TFR scatter $\sigma_{\rm int}$ show no improvement over the isotropic model without a zero-point dipole, though the Bayesian evidence favours the anisotropic models with odds of $877\!:\!1$.
• Figure 3: Comparison of the inferred zero-point dipole in the TFR and SN samples. The contours show the $1\sigma$ and $2\sigma$ confidence regions.
• Figure 4: Summary of the inferred zero-point dipole for each catalogue, given by its magnitude $\Delta_{\rm ZP}$ and direction in Galactic coordinates $(\ell, b)$, compared with literature estimates: the CF4 TFR measurement Boubel_2025, the quasar dipole Secrest_2022, the cluster scaling-relation dipole Migkas_2021, the CF4 bulk flow Watkins_2023, the Pantheon+ dipole (Sorrenti_2023, their $z < 0.05$ sample), and the Local Group velocity in the CMB frame Planck_2020. For the latter four, we plot the opposite direction to that reported, as our dipole is defined in the zero-point rather than in peculiar velocities. We show the inferred magnitude only for Boubel_2025, as the remaining works measure dipoles in different quantities that we do not convert. All results are reported in the CMB frame. Error bars indicate the 16th and 84th percentiles.
• Figure 5: Comparison of the inferred dipole in the CF4 TFR W1 subsample under two different priors: uniform in the dipole magnitude or uniform in Cartesian components of the dipole. The latter induces a prior that favours larger magnitudes, resulting in a higher posterior dipole amplitude. The inferred direction is largely insensitive to the prior choice. Contours show the $1\sigma$ and $2\sigma$ confidence regions.