Curvature Perturbations from First-Order Phase Transitions: Implications to Black Holes and Gravitational Waves

We employ a covariant formalism to study the evolution of cosmological perturbations during a first-order phase transition, addressing in particular their gauge dependence that have been overlooked so far. Our results reveal that non-covariant treatments employed in previous studies can substantially overestimate the production of primordial black holes and scalar-induced gravitational waves. Once gauge dependencies are properly accounted for, we find that both effects occur at significantly lower levels than previously estimated.