Constraining the local variance of $H_0$ from directional analyses

Abstract: We evaluate the local variance of the Hubble Constant $H_0$ with low-z Type Ia Supernovae (SNe). Our analyses are performed using a hemispherical comparison method in order to test whether taking the bulk flow motion into account can reconcile the measurement of the Hubble Constant $H_0$ from standard candles ($H_0 = 73.8 \pm 2.4 \; \mathrm{km \; s}^{-1}\; \mathrm{Mpc}^{-1}$) with that of the Planck's Cosmic Microwave Background data ($H_0 = 67.8 \pm 0.9 \; \mathrm{km \; s}^{-1} \mathrm{Mpc}^{-1}$). We obtaina Hubble Constant maximal variance of $\delta H_0 = (2.30 \pm 0.86) \; \mathrm{km \; s}^{-1} \mathrm{Mpc}^{-1}$ towards the $(l,b) = (315^{\circ},27^{\circ})$ direction. Interestingly, this result agrees with the bulk flow direction estimates found in the literature, as well as previous evaluations of the $H_0$ variance due to the presence of nearby inhomogeneities. We assess the statistical significance of this result with different prescriptions of Monte Carlo simulations, obtaining moderate statistical significance, i.e., $68.7$\% confidence level (CL) for such variance. Furthermore, we test the hypothesis of a higher $H_0$ value in the presence of a bulk flow velocity dipole, finding some evidence for this result which, however, cannot be claimed to be significant due to the current large uncertainty in the SNe distance modulus. Then, we conclude that the tension between different $H_0$ determinations can plausibly be caused to the bulk flow motion of the local Universe, even though the current incompleteness of the SNe data set, both in terms of celestial coverage and distance uncertainties, does not allow a high statistical significance for these results or a definitive conclusion about this issue.