Abstract
The discrepancy between estimates of the Hubble Constant ($H_0$) measured
from local ($z 0.1$) 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 $27 2$ %.
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 $50$ 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 $< 0.1 \,km\,s^-1 Mpc^-1$
difference in the sample mean estimate compared to the value uncorrected for
peculiar velocities. Our best estimate is then $74.9 \,km\,s^-1
Mpc^-1$. Using the mock data, the systematic uncertainty from these peculiar
velocity corrections is estimated to be $0.3 \,km\,s^-1 Mpc^-1$. The
dominant source of uncertainty in our estimate instead relates to Cepheid-based
calibrations of distance moduli ($1.7 \,km\,s^-1 Mpc^-1$) and SN
photometry ($0.7 \,km\,s^-1 Mpc^-1$).
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