A smoking gun from the power spectrum dipole for elastic interactions in the dark sector

Models with pure momentum exchange in the dark sector have been shown to provide a promising scenario to tackle the tension in the clustering inferred from high- and low-redshift probes. A distinctive feature of these models is that only the Euler equation for the dark matter component is modified and the correction is such that the net effect can be associated to an additional friction determined by the interaction rate. In this work, we show that the strength of the interaction parameter needed to resolve the $\sigma_8$ tension could be detected from the dipole of the matter power spectrum that is expected to be measured in upcoming surveys.