Peculiar-velocity surveys measure how galaxies move relative to the smooth cosmic expansion, and the standard model makes a firm statistical promise: bulk flows, the coherent average motion of all galaxies in a large volume, should shrink steadily with volume size, dropping to modest amplitudes beyond a couple hundred megaparsecs as the contributions of individual structures average out (Feldman et al. 2010). The promise follows directly from Gaussian initial conditions and linear growth; it is not adjustable.
The measured flows break it. Analyses of peculiar-velocity catalogs, culminating in CosmicFlows-4, find coherent bulk motion of 400 to 600 km/s toward the Centaurus-Vela region persisting across volumes hundreds of megaparsecs deep, roughly twice the ΛCDM expectation at those scales (Kashlinsky et al. 2012; CosmicFlows-4 analyses). A flow that fast and that coherent requires either an attractor mass beyond anything cataloged, initial conditions with more large-scale power than inflation provides, or motion whose source is not gravitational infall at all. Each option violates a different load-bearing assumption, which is why the bulk-flow excess has resisted absorption for over a decade.
The standing is firm on the measurement side and unsettled on the interpretation. DESI and 4MOST peculiar-velocity programs will multiply the tracer counts and extend the reach of the flow measurements, deciding whether the coherence finally rolls over at some depth or continues toward the gigaparsec scales where no standard explanation survives.