Updates on dipolar anisotropy in local measurements of the Hubble constant from Cosmicflows-4

Abstract

We investigate the angular anisotropy of the Hubble constant using the Cosmicflows-4 catalogue, with particular emphasis on three issues often treated only implicitly in the literature: the statistical formulation of the Hubble--Lema\^{i}tre relation, the internal consistency of the working sample, and the role of peculiar-velocity corrections. Rather than working in luminosity-distance space, we adopt a logarithmic formulation based directly on distance moduli, thereby preserving the Gaussian error properties of the measured quantities. We first subject the catalogue to internal consistency tests, including the depth dependence of $\langle \log H_0 \rangle$ and the behaviour of residual skewness and kurtosis across radial shells, and use these diagnostics to define conservative subsamples minimally affected by selection effects, namely $\mu \in [31,36]$ and $z \in [0.03,0.06]$. Within these ranges, we reconstruct angular maps of $\log H_0$ and fit them with a spherical-harmonic expansion up to octupole order. We find a statistically significant anisotropic signal in the uncorrected CF4 data, dominated by a dipole and favoured over a monopole-only model by Bayesian evidence. However, when peculiar-velocity-corrected data are used, the anisotropy amplitude is strongly reduced, especially at lower depths, while only a weaker residual signal survives at larger distances. We also test for a monotonic radial evolution of the dipole, as expected in some differential-expansion scenarios, but find no robust evidence for such a trend. These results indicate that the anisotropy is driven primarily by local velocity flows and catalogue/survey structure, rather than by a large-scale breakdown of isotropic expansion. Finally, we show that although such anisotropy may affect local determinations of $H_0$, its impact on the global Hubble tension is likely limited.