Distinguishing thermal histories of dark matter from structure formation

It is important to understand the implications of current observational constraints and potential signatures on the thermal history of dark matter. In this paper, we build the connection between the present-day velocities and the production mechanism of dark matter and find that the current observation on structure formation can be imposed to constrain the decoupling temperatures and the phase-space distribution of dark matter. We further explore the potential of distinguishing different possible thermal histories of dark matter with hypothetical future observational data. Using the freeze-in/-out scenarios as templates, we find that future precision data may uniquely identify the allowed parameter spaces for freeze-in and freeze-out, or even completely rule out one of the scenarios. This method can be more generally applied to other scenarios.