Boosted dark matter from primordial black holes produced in a first-order phase transition

During a cosmological first-order phase transition in a dark sector, fermion dark matter particles $\chi$ can form macroscopic Fermi balls that collapse to primordial black holes (PBHs) under certain conditions. The evaporation of the PBHs produces a boosted $\chi$ flux, which may be detectable if $\chi$ couples to visible matter. We consider the interaction of $\chi$ with electrons, and calculate signals of the dark matter flux in the XENON1T, XENONnT, Super-Kamiokande and Hyper-Kamiokande experiments. A correlated gravitational wave signal from the phase transition can be observed at THEIA and $\mu$Ares. An amount of dark radiation measurable by CMB-S4 is an epiphenomenon of the phase transition.