Dark Matter from Decaying Topological Defects

We study dark matter production by decaying topological defects, in particular cosmic strings. In topological defect or "top-down" (TD) scenarios, the dark matter injection rate varies as a power law with time with exponent $p-4$. We find a formula in closed form for the yield for all $p < 3/2$, which accurately reproduces the solution of the Boltzmann equation. We investigate two scenarios ($p=1$, $p=7/6$) motivated by cosmic strings which decay into TeV-scale states with a high branching fraction into dark matter particles. For dark matter models annihilating either by s-wave or p-wave, we find the regions of parameter space where the TD model can account for the dark matter relic density as measured by Planck. We find that topological defects can be the principal source of dark matter, even when the standard freeze-out calculation under-predicts the relic density and hence can lead to potentially large "boost factor" enhancements in the dark matter annihilation rate. We examine dark matter model-independent limits on this scenario arising from unitarity and discuss example model-dependent limits coming from indirect dark matter search experiments. In the four cases studied, the upper bound on $G\mu$ for strings with an appreciable channel into TeV-scale states is significantly more stringent than the current Cosmic Microwave Background limits.