Effective theory of self-interacting dark matter

We present an effective nonrelativistic theory of self-interacting dark matter. We classify the long-range interactions and discuss how they can be generated from quantum field theories. Generic dark sectors can generate singular potentials. We show how to consistently renormalize such potentials and apply this to the calculation of the Sommerfeld enhancement of dark matter interactions. We explore further applications of this enhancement to astrophysical probes of dark matter including the core vs cusp problem.