Cosmic flows and the expansion of the Local Universe from nonlinear   phase-space reconstructions
  This work investigates the impact of cosmic flows and density perturbations on Hubble constant $H_0$ measurements using nonlinear phase-space reconstructions of the Local Universe (LU). In particular, we rely on 25 constrained N-body simulations of the LU using the 2MRS galaxy sample within distances of 90 Mpc/h. These have been randomly extended up to volumes enclosing 360 Mpc/h with augmented Lagrangian perturbation theory (750 simulations in total), accounting in this way for gravitational mode coupling from larger scales, correcting for periodic boundary effects, and estimating systematics of missing attractors ($\sigma_{\rm large}=134$ km/s). We report on Local Group speed reconstructions, which are compatible with CMB-dipole measurements: $|v_{\rm LG}|=685\pm137$ km/s. The direction $(l,b)=(260.5\pm 13.3,39.1\pm 10.4)^\circ$ is compatible with observations after considering the variance of large scales. Accounting for large scales, our local bulk flow estimations assuming a $\Lambda$CDM model are compatible with estimates based on velocity data derived from the Tully-Fisher relation.   We focus on low redshift supernova measurements ($0.01<z<0.025$), which have been found to disagree with probes at larger distances. Our analysis indicates that there are two effects contributing to this tension. First, the anisotropic distribution of supernovae aligns with the velocity dipole and induces a systematic boost in $H_0$. Second, a divergent region surrounding the Virgo Supercluster is responsible for an additional positive bias in $H_0$. Taking these effects into account yields a correction of $\Delta H_0=-1.76 \pm 0.21 $ km/s/Mpc, thereby reducing the tension between local probes and more distant probes. Effectively $H_0$ is lower by about $2\%$. 
Steffen Hess and Francisco-Shu Kitaura
astro-ph.CO