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We investigate the first-order phase transition catalyzed by primordial black holes~ (PBHs) in the early Universe. We find that super-horizon curvature perturbations generated in this scenario lead to the production of gravitational waves when the scalar modes re-enter the horizon. If PBHs with masses about 10^-13M_ constitute all dark matter, the first-order electroweak phase transition catalyzed by PBHs can explain the gravitational wave signal observed by pulsar timing array collaborations without the overproduction of PBHs.
Zeng et al. (2024) studied this question.