![](https://www.physics.uci.edu/sites/default/files/default_images/blank-separator-rev.png)
![](https://www.physics.uci.edu/sites/default/files/default_images/separator_3.png)
Abstract: It is important to understand the implications of current observational constraints and potential signatures on the thermal history of dark matter. In this work, 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.