Primordial Black Holes and Gravitational Waves in Extensions of the Standard Model

We investigate the phenomenology of a Standard Model extension incorporating an inert scalar doublet and a gauged $U(1{)}_{B-L}$ symmetry. Our analysis reveals regions of the parameter space that support strong first-order phase transitions, including cases featuring two successive transitions. Each transition can generate a stochastic gravitational wave background within the sensitivity reach of upcoming experiments. Remarkably, the high-scale transition may also produce primordial black holes with appreciable abundance.