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

Abstract

Understanding whether primordial black holes form during strong first-order phase transition (FOPT) is a crucial open question in cosmology. We address this using a fully covariant formalism to study cosmological perturbations, highlighting previously overlooked gauge dependencies. We show that non-covariant treatments can overestimate primordial black holes and scalar-induced gravitational waves. Once gauge dependencies are accounted for, both signals are strongly suppressed, with direct implications for the FOPT interpretation of the Pulsar Timing Array signal.

Published in PRL (5 pages, 4 figures). Promised companion paper added as Supplemental Material (14 pages, 6 figures). Results reproducible with public code: https://github.com/YannGou/deltaPT2.0