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 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 acts as a proxy for peculiar velocity ($v_{pec}$) by quantifying density gradients along a line-of-sight. $\Delta \phi_{+-}$ is found to correlate strongly with local $H_{0}$ estimates from Union 2.1 Type Ia SNe ($0.02 < z < 0.04$). Density structures on scales of $\sim 50$ Mpc are found to correlate most strongly with $H_{0}$ estimates in both the observational data and in mock data from the MDPL2-Galacticus simulation. Interpolating SN Ia $H_{0}$ estimates to their $\Delta \phi_{+-} = 0$ values, we can correct for the effects of density structure on the local $H_{0}$ estimates, even in the presence of biased peculiar velocities. For these particular observational data, we reveal a $< 0.1 \,\rm km\,s^{-1} Mpc^{-1}$ difference in the sample mean estimate compared to the value uncorrected for peculiar velocities. Our best estimate is then $74.9 \,\rm km\,s^{-1} Mpc^{-1}$. Using the mock data, the systematic uncertainty from these peculiar velocity corrections is estimated to be $0.3 \,\rm km\,s^{-1} Mpc^{-1}$. The dominant source of uncertainty in our estimate instead relates to Cepheid-based calibrations of distance moduli ($1.7 \,\rm km\,s^{-1} Mpc^{-1}$) and SN photometry ($0.7 \,\rm km\,s^{-1} Mpc^{-1}$).