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This work investigates the impact of cosmic flows and density perturbationson Hubble constant $H_0$ measurements using nonlinear phase-spacereconstructions of the Local Universe (LU). In particular, we rely on 25constrained N-body simulations of the LU using the 2MRS galaxy sample withindistances of 90 Mpc/h. These have been randomly extended up to volumesenclosing 360 Mpc/h with augmented Lagrangian perturbation theory (750simulations in total), accounting in this way for gravitational mode couplingfrom larger scales, correcting for periodic boundary effects, and estimatingsystematics of missing attractors ($\sigma_{\rm large}=134$ km/s). We report onLocal Group speed reconstructions, which are compatible with CMB-dipolemeasurements: $|v_{\rm LG}|=685\pm137$ km/s. The direction $(l,b)=(260.5\pm13.3,39.1\pm 10.4)^\circ$ is compatible with observations after considering thevariance of large scales. Accounting for large scales, our local bulk flowestimations assuming a $\Lambda$CDM model are compatible with estimates basedon velocity data derived from the Tully-Fisher relation.  We focus on low redshift supernova measurements ($0.01<z<0.025$), which havebeen found to disagree with probes at larger distances. Our analysis indicatesthat there are two effects contributing to this tension. First, the anisotropicdistribution of supernovae aligns with the velocity dipole and induces asystematic boost in $H_0$. Second, a divergent region surrounding the VirgoSupercluster is responsible for an additional positive bias in $H_0$. Takingthese 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 distantprobes. Effectively $H_0$ is lower by about $2\%$.

Cosmic flows and the expansion of the Local Universe from nonlinear phase-space reconstructions