Primordial black holes as a natural consequence of scale-invariance

We show that a scale-invariant $U(1)$ gauge theory can naturally realize large curvature perturbations around the end of thermal inflation, seeding the formation of primordial black holes (PBHs). The allowed nonminimal gravitational interaction $\xi$ of the Higgs field induces a Hubble-scale negative mass-squared term for positive $\xi \sim \mathcal{O}(1)$, and triggers a second order phase transition that ends thermal inflation while keeping the extra $e$-folds small. This sharp contrast to the minimally coupled case allows the gauge coupling to be much smaller than unity. It turns out that field fluctuations are dominated by thermal fluctuations around the onset of the phase transition, and sufficiently amplified to produce an appreciable amount of PBHs with a wide range of possible masses. The associated scalar-induced gravitational waves (GWs) are accompanied by cosmic-string induced GWs coming from the breaking of the $U(1)$ symmetry. As a result, the generated PBH population can have a correlated GW signature relevant to pulsar timing arrays, space-based interferometers, or ground-based detectors.