  Low energy interactions between particles are often characterised by elastic
scattering. Just as electrons undergo Thomson scattering with photons, dark
matter particles may experience an analogous form of momentum exchange with
dark energy. We investigate the influence such an interaction has on the
formation of linear and nonlinear cosmic structure, by running for the first
time a suite of N-body simulations with different dark energy equations of
state and scattering cross sections. In models where the linear matter power
spectrum is suppressed by the scattering, we find that on nonlinear scales the
power spectrum is strongly enhanced. This is due to the friction term
increasing the efficiency of gravitational collapse, which also leads to a
scale-independent amplification of the concentration and mass functions of
halos. The opposite trend is found for models characterised by an increase of
the linear matter power spectrum normalisation. More quantitatively, we find
that power spectrum deviations at nonlinear scales ($k \approx 10\, h/$Mpc) are
roughly ten times larger than their linear counterparts, exceeding $100%$ for
the largest value of the scattering cross section considered in the present
work. Similarly, the concentration-mass relation and the halo mass function
show deviations up to $100%$ and $20%$, respectively, over a wide range of
masses. Therefore, we conclude that nonlinear probes of structure formation
might provide much tighter constraints on the scattering cross section between
dark energy and dark matter as compared to the present bounds based on linear
observables.
