Galaxy flows within 8,000 km/s from Numerical Action methods

The trajectories since z=4 of systems of galaxies (`halos') with cz < 8,000 km/s are found through Numerical Action reconstructions. A set of 9,719 halos from a 2MASS group catalog and Cosmicflows-3 catalogs are given attention. Present distances are adjusted to minimize departures from observed redshifts. For those with the most precisely determined distances, compromises are made between distance and redshift agreement. $H_0$ is varied from 69 to 77 km s$^{-1}$ Mpc$^{-1}$ with $\Omega_m$ set by the baryon acoustic oscillation constraint from the Planck Satellite. A best fitting amplitude of the mass-to-light relation is found. A uniform density associated with the interhalo medium accounts for the matter not in halos. The solution paths provide the histories of the formation of the nearby large structures and depict how the voids emptied. Assuming no local over/underdensity, the best model has $H_0=73$ km s$^{-1}$ Mpc$^{-1}$ with nearly the same density arising from interhalo matter (IHM) as from halos. We examine local over/underdensities by varying the IHM density and find a valley of best fit models along $H_0 = 73.0 (1 + 0.165\delta)$ km s$^{-1}$ Mpc$^{-1}$. Friedmann models with distinct densities internal and external to the study region give a similar relationship. The fraction of matter in the IHM seen in n-body simulations roughly matches that in our $H_0=72$ scenario. Videos have been created to visualize the complexities of formation of large-scale structures. Standard n-body calculations starting from the first time-steps as tests of the NAM solutions, and continue until cosmic scale factor $a=2$ provide glimpses into the future.