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  • Letter
  • Open Access

Gauge-invariant bubble nucleation and gravitational waves from first-order electroweak phase transitions

Jie Liu, Renhui Qin*, and Ligong Bian†

  • Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 401331, People’s Republic of China

  • *Contact author: 20222701021@stu.cqu.edu.cn
  • †Contact author: lgbycl@cqu.edu.cn
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Phys. Rev. D 114, L031703 – Published 31 August, 2026

DOI: https://doi.org/10.1103/45ks-x47h

Abstract

A long-standing problem in electroweak phase transition studies is the spurious gauge dependence of bubble nucleation rate calculations, which introduces large systematic uncertainties in predictions of gravitational waves and related cosmological phenomena. We address this issue by presenting a systematic study of gauge-invariant bubble nucleation within a phenomenologically realistic effective field theory framework. Using the three-dimensional thermal effective field theory formalism with a consistent power-counting scheme, we rigorously establish the gauge invariance of the physical nucleation rate up to two-loop order. This proof eliminates the gauge-parameter dependence of key phase transition parameters, providing a robust theoretical foundation for precise calculations of gravitational waves, electroweak baryogenesis, and primordial magnetogenesis.

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Phys. Rev. D 114, L031703– Published 31 August, 2026
  • Received 4 January 2026
  • Accepted 6 August 2026
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