Self-interacting dark matter scattering rates through cosmic time

We estimate the rate of dark matter scattering in collapsed structures throughout the history of the Universe. If the scattering cross-section is velocity independent, then the canonical picture is correct that scatterings occur mainly at late times. The scattering rate peaks slightly at redshift z similar to 6, and remains significant today. Half the scatterings occur after z similar to 1, in structures more massive than 1012M(circle dot). Within a factor of 2, these numbers are robust to changes in the assumed astrophysics, and the scatterings would be captured in cosmological simulations. However, for particle physics models with a velocity-dependent cross-section (as for Yukawa potential interactions via a massive mediator), the scattering rate peaks before z similar to 20, in objects with mass less than or similar to 10(4)M(circle dot). These precise values are sensitive to the redshift-dependent mass-concentration relation and the small-scale cut-off in the matter power spectrum. In extreme cases, the qualitative effect of early interactions may be reminiscent of warm dark matter and strongly affect the subsequent growth of structure. However, these scatterings are being missed in existing cosmological simulations with limited mass resolution.