The impact of anisotropic sky-sampling on the Hubble constant in numerical relativity

We study the impact of nearby inhomogeneities on an observer's inference of the Hubble constant. Large-scale structures induce a dependence of cosmological parameters on observer position as well as an anisotropic variance of those parameters across an observer's sky. While the former has been explored quite thoroughly, the latter has not. Incomplete sampling of an anisotropic sky could introduce a bias in our cosmological inference if we assume an isotropic expansion law. In this work, we use numerical relativity simulations of large-scale structure combined with ray tracing to produce synthetic catalogs mimicking the low-redshift Pantheon supernova dataset. Our data contains all general-relativistic contributions to fluctuations in the distances and redshifts along geodesics in the simulation. We use these synthetic observations to constrain $H_0$ for a set of randomly-positioned observers. We study both the dependence on observer position as well as the impact of rotating the sample of supernovae on the observer's sky. We find a 1--2\% variance in $H_0$ between observers when they use an isotropic sample of objects. However, we find the inferred value of $H_0$ can vary by up to 4--6\% when observers simply rotate their Pantheon data set on the sky. While the variances we find are below the level of the ``Hubble tension'', our results may suggest a reduction in the significance of the tension if anisotropy of expansion can be correctly accounted for.