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  • Open Access

Subcritical bubble prehistory in a weak first-order phase transition

Guangshang Chen2, Yang Xiao1,*, Jin Min Yang1,3, and Yang Zhang1,†

  • 1School of Physics, Henan Normal University, Xinxiang 453007, People’s Republic of China
  • 2Key Laboratory of Particle Physics and Particle Irradiation (MOE), Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, 266237, Shandong, China
  • 3Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

  • *Contact author: xiaoyangphy@gmail.com
  • †Contact author: zhangyang2025@htu.edu.cn

Phys. Rev. D 114, 015031 – Published 22 July, 2026

DOI: https://doi.org/10.1103/3qbc-h73q

Abstract

Standard calculations of cosmological first-order phase transitions usually assume critical bubbles to nucleate on a homogeneous symmetric vacuum background. However, this assumption can fail in weak transitions, where thermal fluctuations trigger subcritical bubbles before the standard nucleation temperature Tn. Motivated by this possibility, we systematically examine whether the homogeneous nucleation background approximation is self-consistent. By evolving the Gelmini-Gleiser subcritical bubble kinetics and comparing it with the standard critical bubble nucleation picture, we identify the parameter regions in which the background becomes apparently mixed. A detailed scan of these regions shows that sizable subcritical volume fractions arise when the two phases are nearly degenerate at Tn, the potential barrier is low, the difference of free energy between the symmetric and broken phases is moderate and the transition strength is weak. Within this simplified phenomenological kinetic framework, this scan further calibrates a practical reference criterion, log10f^ξ(Tn)≃−1.95, for percent level subcritical bubble volume fractions. Parameter points above this boundary should be treated as mixed background candidates rather than as ordinary homogeneous bounce points.

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