Average peculiar velocity field, ⟨ υ_pec ⟩, normalized over , as a function of the Universe scale factor, R, for (red solid line) and 1000 (green solid line). We observe that within the linear regime, peculiar velocities conform with the rms-velocity law of statistical physics (i.e., ) given by Eq. (14). In both curves, the receding part arising for (z ≤ 4) signals the onset of deviations from the rms-velocity law due to the collapse of linear approximation and Hubble drag.