Testing anisotropic Hubble expansion

The cosmological principle asserting the large-scale uniformity of the Universe is a testable assumption of the standard cosmological model. We explore the constraints on anisotropic expansion provided by measuring directional variation in the Hubble constant, $H_0$, derived from differential zeropoint measurements of the Tully-Fisher distance estimator. We fit various models for directional variation in $H_0$ using the Tully-Fisher dataset from the all-sky Cosmicflows-4 catalog. The best-fit dipole variation has an amplitude of 0.063 $\pm$ 0.016 mag in the direction ($\ell,b$) = (142 $\pm$ 30$^{\circ}$, 52 $\pm$ 10$^{\circ}$). If this were due to anisotropic expansion it would imply a 3% variation in $H_0$, corresponding to $\Delta H_0$ = 2.10 $\pm$ 0.53 km/s/Mpc if $H_0$ = 70 km/s/Mpc, with a significance of 3.9$\sigma$. A model that includes this $H_0$ dipole is only weakly favored relative to a model with a constant $H_0$ and a bulk motion of the volume sampled by Cosmicflows-4 that is consistent with the standard $\Lambda$CDM cosmology. However, we show that with the expected Tully-Fisher data from the WALLABY and DESI surveys it should be possible to detect a 1% $H_0$ dipole anisotropy at 5.8$\sigma$ confidence and to distinguish it from the typical bulk flow predicted by $\Lambda$CDM over the volume of these surveys.