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  • Open Access

How large are curvature perturbations from slow first-order phase transitions? A gauge-invariant analysis

Xiao Wang1, Csaba Balázs1, Ran Ding*, and Chi Tian2,†

  • 1School of Physics and Astronomy, Monash University, Melbourne 3800 Victoria, Australia
  • 2School of Physics, Anhui University, 111 Jiulong Road, Hefei, Anhui, China 230601

  • *Contact author: dingran@mail.nankai.edu.cn
  • †Contact author: ctian@ahu.edu.cn
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Phys. Rev. D 113, 123026 – Published 11 June, 2026

DOI: https://doi.org/10.1103/y9ks-n9sv

Abstract

When strongly supercooled cosmological first-order phase transitions (FOPTs) are sufficiently slow, superhorizon inhomogeneities can be generated. We compute these superhorizon curvature perturbations by employing a gauge-invariant, multifluid formalism. By resolving the gauge ambiguities inherent in conventional separate-universe simulations, we demonstrate that primordial black holes are unlikely to be produced by these superhorizon inhomogeneities. We also derive a fitting formula for the resulting curvature perturbations and discuss potential observational constraints on FOPTs imposed by limits on primordial curvature perturbations and associated scalar-induced gravitational waves.

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Phys. Rev. D 113, 123026– Published 11 June, 2026
  • Received 13 February 2026
  • Accepted 30 April 2026
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