The effects of peculiar velocities in SN Ia environments on the local
  $H_0$ measurement
  The discrepancy between estimates of the Hubble Constant ($H_0$) measured
from local ($z \lesssim 0.1$) scales and from scales of the sound horizon is a
crucial problem in modern cosmology. Peculiar velocities ($v_{pec}$) of
standard candle distance indicators can systematically affect local $H_0$
measurements. We here use 2MRS galaxies to measure the local galaxy density
field, finding a notable $z$ < 0.05 under-density in the SGC-6dFGS region of 27
$\pm$ 2 %. However, no strong evidence for a 'Local Void' pertaining to the
full 2MRS sky coverage is found. Galaxy densities are used to measure a density
parameter, $\Delta \phi_{+-}$, which we introduce as a proxy for $v_{pec}$
which quantifies density gradients along a SN line-of-sight. $\Delta \phi_{+-}$
is found to correlate with local $H_0$ estimates from 88 Pantheon SNeIa (0.02 <
$z$ < 0.05). Density structures on scales of $\sim$ 50 Mpc are found to
correlate strongest with $H_0$ estimates in both the observational data and in
mock data from the MDPL2-Galacticus simulation. Using trends of $H_0$ with
$\Delta \phi_{+-}$, we can correct for the effects of density structure on
local $H_0$ estimates, even in the presence of biased $v_{pec}$. However, the
difference in the inferred $H_0$ estimate with and without the peculiar
velocity correction is limited to < 0.1 %. We conclude that accounting for
environmentally-induced peculiar velocities of SNIa host galaxies does not
resolve the tension between local and CMB-derived $H_0$ estimates.
