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Galaxies in the Universe are not scattered randomly: neighboring ones move in the same direction, like a school of fish, while distant ones each go their own way. Where the boundary between 'together' and 'apart' lies has been unclear until now. Astronomers have devised a new measure — the scale at which the average motion of galaxies along the line connecting a pair stops being coherent and starts contradicting each other.

This scale is called the velocity coherence scale. It can be computed via a special quantity — the sphere-averaged trace of the velocity correlation tensor. Sounds complicated, but the idea is simple: take a sphere around a point and see how galaxies inside it move relative to the center. On small spheres, they on average move away from or toward the center in a coordinated way. On larger spheres, the motion becomes chaotic, like a crowd in a square after a concert.

The most interesting part is that this scale is almost independent of time. In an expanding Universe, it remains the same in comoving coordinates, as if the ruler grew with space itself. Therefore, it can be used as a 'standard ruler' for measuring cosmic distances. It is also closely related to the moment when matter and radiation densities in the Universe became equal — a key event in its history.

Currently, measurement precision is limited: galaxy velocities are known less accurately than their positions. But new sky surveys, already operating or in preparation, will allow refining this scale. Then cosmologists will have another reliable tool to test our understanding of the Universe's structure.