Black holes seeding cosmological phase transitions

We consider a generic first-order phase transition at finite temperature and investigate to what extent a population of primordial black holes, of variable masses, can affect the rate of bubble nucleation. Using a thin-wall approximation, we construct the Euclidean configurations that describe transition at finite temperature. After the transition, the remnant black hole mass is dictated dynamically by the equations of motion. The transition exponent is computed and displays an explicit dependence on temperature. We find the configuration with the lowest Euclidean action to be static and $O(3)$ symmetric; therefore, the transition takes place via thermal excitation. The transition exponent exhibits a strong dependence on the seed mass black hole, $M_+$, being almost directly proportional. A new nucleation condition in the presence of black holes is derived and the nucleation temperature is compared to the familiar flat-space result, i.e. $S_3/T$. For an electroweak-like phase transition it is possible to enhance the nucleation rate if $M_+ \lesssim 10^{15} M_{\rm P}$. Finally, we outline the possible transition scenarios and the consequences for the power spectrum of stochastic gravitational waves produced due to the first-order phase transition.