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

Abstract: Claims of 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 (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 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. Inferring a more general bulk flow curve we find results fully consistent with expectations from the standard cosmological model.