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We consider a cosmological model with an interaction between dark matter anddark energy which leaves the background cosmology unaffected and only affectsthe evolution of the perturbations. This is achieved by introducing a couplinggiven in terms of the relative velocities of dark matter and dark energy. Thisinteraction has the distinctive feature of appearing predominantly on smallscales, where peculiar velocities can become important. We confront thepredictions of the model to cosmological observations and find a potentialalleviation of the known tension in the amplitude of density perturbations asmeasured by low redshift galaxy surveys and the Planck data. The model alsopredicts a shift in the turnover of the matter power spectrum which does notdepend on the horizon at equality (fixed by the background cosmology and, thus,unaffected by the perturbations) and is entirely due to the interaction betweendark matter and dark energy. A bias in the peculiar velocity between baryonsand dark matter is also shown to be a unique feature of this type ofinteractions in the dark sector.

On structure formation from a small-scales-interacting dark sector