Nonperturbative Phenomena in Self-Interacting Dark Matter

The vanilla LCDM model of cosmology, in spite of being highly successful in explaining observations across various cosmological length scales, is plagued by a few issues at small, namely, the galactic and sub-galactic scales. Self-interacting dark matter is a promising candidate that can address these issues. While nonlinear baryonic physics plays an important role at these scales, computer simulations of self-interacting dark matter have been shown to explain observations fairly well. An interesting consequence of interactions among dark matter particles is the nonrelativistic, nonperturbative phenomena, like the Sommerfeld effect, large self-scattering etc. I shall review this topic and present my works on a few nontrivial results of these phenomena in dark matter indirect detection and halo dynamics.