Hot and heavy dark matter from a weak scale phase transition

We point out that dark matter which is produced non-adiabatically in a phase transition (PT) with fast bubble walls receives a boost in velocity which leads to long free-streaming lengths. We find that this could be observed via the suppressed matter power spectrum for dark matter masses around 108 − 109 GeV and energy scales of the PT around 102 − 103 GeV. The PT should take place at the border of the supercooled regime, i.e. approximately when the Universe becomes vacuum dominated. This work offers novel physics goals for galaxy surveys, Lyman-α, stellar stream, lensing, and 21-cm observations, and connects these to the gravitational waves from such phase transitions, and more speculatively to possible telescope signals of heavy dark matter decay.