Non-linear structure formation with elastic interactions in the dark sector

Cosmological models where dark matter interacts with dark energy via a pure momentum transfer and with no energy exchange (i.e. elastic) provide compelling scenarios for addressing the apparent lack of structures at low redshift. In particular, it has been shown that measurements of $S_8$ may show a statistically significant preference for the presence of elastic interactions. In this work we implement a specific realisation of these scenarios into an $N$-body code to explore the non-linear regime. We include two populations of particles to describe the interacting dark matter and the non-interacting baryons respectively. On linear scales we recover the suppression of structures obtained from Boltzmann codes, while non-linear scales exhibit an enhancement of the matter power. We find that fewer massive halos are formed at low redshift as a consequence of the elastic interaction and that dark matter halos are more compact than in the standard model. Furthermore, the ratio of dark matter and baryons density profiles is not constant. Finally, we corroborate that baryons efficiently cluster around dark matter halos so they provide good tracers of the dark matter velocity field despite the presence of the interaction. This shows that the interaction is not sufficiently strong as to disrupt virialised structures.