  We demonstrate that self-interacting dark matter models with interactions
mediated by light particles can have significant deviations in the matter
power-spectrum and detailed structure of galactic halos when compared to a
standard cold dark matter scenario. While these deviations can take the form of
suppression of small scale structure that are in some ways similar to that of
warm dark matter, the self-interacting models have a much wider range of
possible phenomenology. A long-range force in the dark matter can introduce
multiple scales to the initial power spectrum, in the form of dark acoustic
oscillations and an exponential cut-off in the power spectrum. Using
simulations we show that the impact of these scales can remain observationally
relevant up to the present day. Furthermore, the self-interaction can continue
to modify the small-scale structure of the dark matter halos, reducing their
central densities and creating a dark matter core. The resulting phenomenology
is unique to this type of models.
