Unitarity Bounds and the Cuspy Halo Problem

Conventional cold dark matter cosmological models predict cuspy halos which are in apparent conflict with observations. We show that unitarity arguments imply interesting constraints on two proposals to address this problem: collisional dark matter and strongly annihilating dark matter. Efficient scattering in both implies $m\lesssim 12\mathrm{GeV}$ and $m\lesssim 25\mathrm{GeV}$, respectively. We also show that the strong annihilation in the second scenario implies the presence of elastic scattering. Recent evidence suggests a collisional scenario where the cross section scales inversely with velocity—we argue superelastic processes are likely involved. Exceptions and implications for searches are discussed.