Dark Matter from Exponential Growth

We propose a novel mechanism for the production of dark matter (DM) from a thermal bath, based on the idea that DM particles $\chi$ can transform heat bath particles $\psi$: $\chi \psi \rightarrow \chi \chi$. For a small initial abundance of $\chi$ this leads to an exponential growth of the DM number density, in close analogy to other familiar exponential growth processes in nature. We demonstrate that this mechanism complements freeze-in and freeze-out production in a generic way, opening new parameter space to explain the observed DM abundance, and we discuss observational prospects for such scenarios.