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.

Comments: 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