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This project aims to measure both distances and velocities for 100,000 galaxies and so map the visible and dark matter within a billion light-years. It exploits data from the first year of a transformational survey using the European Southern Observatory’s newest facility, which will surpass existing maps by a factor of 10 in volume and 50 in galaxies. The goals are to find the origin of the Milky Way’s motion through space, test predictions for the motions of galaxies on large scales, confirm the Universe becomes smooth on the largest scales, and pave the way for the full five-year survey.

Aim 1: to make the largest and most detailed map to date of galaxy positions and motions in the nearby volume of the Universe, using the 4HS survey of galaxy redshifts and peculiar velocities.

Aim 2: to measure the typical ‘bulk’ (mean) motions of galaxies on scales up to a billion light-years, about 3x the scale of the baryon acoustic oscillations and reaching the largest structures in the Universe.

Aim 3: to trace the asymptotic approach to zero bulk motions with increasing scale, signalling the transition to dynamical homogeneity on the largest scales for the Universe.

• Where are we going, and why? The primary goals of this project are to measure the bulk (mean) motions of galaxies in the nearby Universe and test the standard cosmological model prediction for their variation on the largest scales, where the Universe approaches homogeneity. On the largest scales, the Universe is on average homogeneous, so the gravitational attractions cancel, and the coherent bulk motions measured relative to the cosmological standard of rest set by the cosmic microwave background (CMB) are expected to average to zero. On smaller scales, inhomogeneity (large-scale structure) means that galaxies are typically moving at hundreds of km/s with respect to the CMB. Our own Milky Way is moving at 620 km/s relative to the CMB (Plank Collaboration 2020). However, this motion has still not been fully reconciled with the mass distribution in the local Universe, for two reasons. First, all-sky maps of the cosmic density field as revealed by the distribution of galaxies in space do not yet extend far enough to trace the full extent of the most massive nearby structures. Second, existing maps of the cosmic velocity field are neither extensive enough nor precise enough to trace the scale at which bulk flows converge to the cosmic average. The Milky Way’s motion must be due to larger and more distant structures still to be discovered in the southern hemisphere.

• Why is measuring the bulk motion of galaxies and the approach to homogeneity important? The homogeneity of the universe on sufficiently large scales is a fundamental feature of the standard cosmological model. It is empirically justified by the uniformity observed both in the CMB temperature at very early times and in the distributions of bright galaxies, quasars, and radio sources at intermediate redshifts. However, the approach to homogeneity as a function of scale is a core prediction of the cosmological model that has yet to be robustly tested. This is difficult to do using redshift surveys because galaxies are not only intrinsically biased tracers of the mass distribution, but the selection of galaxies (the bias of the sample) is a function of distance (scale). Moreover, the scale of homogeneity is larger at later times, which exacerbates this problem in the late-time (nearby) Universe, where it is similar to, or larger than, the ~150 Mpc scale of the baryon acoustic oscillations, the largest coherent structures.

• What do we need to do? To test the predicted approach to homogeneity, we thus need to map the density and velocity fields over scales at least 3x larger, out to distances of ~500 Mpc (i.e. the volume within z~0.12). Over this range of scales, the typical bulk motion decreases from several hundred km/s (as for the Milky Way) to 100 km/s. However, measurements of the bulk motion as a function of scale have large uncertainties (and scatter) on scales ≥100 Mpc and are scarce on scales ≥200 Mpc, where they asymptotically approach zero. Precise measurements of bulk motions on all scales out to ~500 Mpc from peculiar velocities offer a clean test of the approach to homogeneity, avoiding the galaxy bias plaguing redshift surveys. 4HS can provide just such a test by determining the overall normalisation of the relation between bulk flow and scale (set by the amplitude of the matter fluctuations produced in the Big Bang) with ~10% precision.