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The existence of critical points for the peculiar velocity field is a naturalfeature of the correlated vector field. These points appear at the junctions ofvelocity domains with different orientations of their averaged velocityvectors. Since peculiar velocities are the important cause of the scatter inthe Hubble expansion rate, we propose that a more precise determination of theHubble constant can be made by restricting analysis to a subsample ofobservational data containing only the zones around the critical points of thepeculiar velocity field, associated with voids and saddle points. Onlarge-scales the critical points, where the first derivative of thegravitational potential vanishes, can easily be identified using the densityfield and classified by the behavior of the Hessian of the gravitationalpotential. We use high-resolution N-body simulations to show that these regionsare stable in time and hence are excellent tracers of the initial conditions.Furthermore, we show that the variance of the Hubble flow can be substantiallyminimized by restricting observations to the subsample of such regions ofvanishing velocity instead of aiming at increasing the statistics by averagingindiscriminately using the full data sets, as is the common approach.

Critical points of the cosmic velocity field and the uncertainties in the value of the Hubble constant