- Open Access
Subcritical bubble prehistory in a weak first-order phase transition
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 . 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 , 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, , 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.
Physics Subject Headings (PhySH)
Article Text
References (42)
- K. Kajantie, M. Laine, K. Rummukainen, and M. E. Shaposhnikov, A nonperturbative analysis of the finite T phase transition in electroweak theory, Nucl. Phys. B493, 413 (1997).
- H. Chen and Y. Jiang, A comprehensive framework for electroweak phase transitions: Thermal history and dynamics from bubble nucleation to percolation, arXiv:2503.00421.
- J. Du, Y. Jiang, and W. Su, Probing the electroweak phase transition in the flipped two-higgs-doublet model at the LHC, arXiv:2605.13939.
- J. Yang, R. Zhou, and L. Bian, Gravitational waves and monopoles dark matter from first-order phase transition, Phys. Lett. B 839, 137822 (2023).
- L. Wang, Inflation, electroweak phase transition, and Higgs searches at the LHC in the two-Higgs-doublet model, J. High Energy Phys. 07 (2022) 055.
- Z.-g. Si, H.-x. Wang, L. Wang, and Y. Zhang, Exploring multi-step electroweak phase transitions in the , Eur. Phys. J. C 85, 273 (2025).
- P. Athron, C. Balázs, A. Fowlie, L. Morris, and L. Wu, Cosmological phase transitions: From perturbative particle physics to gravitational waves, Prog. Part. Nucl. Phys. 135, 104094 (2024).
- X.-F. Han, L. Wang, and Y. Zhang, Dark matter, electroweak phase transition, and gravitational waves in the type ii two-higgs-doublet model with a singlet scalar field, Phys. Rev. D 103, 035012 (2021).
- H.-K. Guo, K. Sinha, D. Vagie, and G. White, Phase transitions in an expanding universe: Stochastic gravitational waves in standard and non-standard histories, J. Cosmol. Astropart. Phys. 01 (2021) 001.
- J. Yang, R. Zhou, and L. Bian, Gravitational waves and monopoles dark matter from first-order phase transition, Phys. Lett. B 839, 137822 (2023).
- V. Vaskonen, Electroweak baryogenesis and gravitational waves from a real scalar singlet, Phys. Rev. D 95, 123515 (2017).
- A. Beniwal, M. Lewicki, M. White, and A. G. Williams, Gravitational waves and electroweak baryogenesis in a global study of the extended scalar singlet model, J. High Energy Phys. 02 (2019) 183.
- Z. Kang, P. Ko, and T. Matsui, Strong first order EWPT & strong gravitational waves in -symmetric singlet scalar extension, J. High Energy Phys. 02 (2018) 115.
- M. Chala, C. Krause, and G. Nardini, Signals of the electroweak phase transition at colliders and gravitational wave observatories, J. High Energy Phys. 07 (2018) 062.
- A. Alves, D. Gonçalves, T. Ghosh, H.-K. Guo, and K. Sinha, Di-Higgs production in the channel and gravitational wave complementarity, J. High Energy Phys. 03 (2020) 053.
- A. Alves, T. Ghosh, H.-K. Guo, K. Sinha, and D. Vagie, Collider and gravitational wave complementarity in exploring the singlet extension of the standard model, J. High Energy Phys. 04 (2019) 052.
- W. Chao, H.-K. Guo, and J. Shu, Gravitational wave signals of electroweak phase transition triggered by dark matter, J. Cosmol. Astropart. Phys. 09 (2017) 009.
- M. Trodden, Electroweak baryogenesis, Rev. Mod. Phys. 71, 1463 (1999).
- J. M. Cline, Baryogenesis, in Les Houches Summer School—Session 86: Particle Physics and Cosmology: The Fabric of Spacetime (2006), p. 9, arXiv:hep-ph/0609145.
- G. A. White, A Pedagogical Introduction to Electroweak Baryogenesis (Morgan and Claypool Publishers, San Rafael, CA, USA, 2016), pp. 2053–2571.
- D. E. Morrissey and M. J. Ramsey-Musolf, Electroweak baryogenesis, New J. Phys. 14, 125003 (2012).
- M. J. Baker and L. Mittnacht, Variations on the vev flip-flop: Instantaneous freeze-out and decaying dark matter, J. High Energy Phys. 05 (2019) 070.
- M. J. Baker, J. Kopp, and A. J. Long, Filtered dark matter at a first order phase transition, Phys. Rev. Lett. 125, 151102 (2020).
- M. J. Baker, M. Breitbach, J. Kopp, and L. Mittnacht, Dynamic freeze-in: Impact of thermal masses and cosmological phase transitions on dark matter production, J. High Energy Phys. 03 (2018) 114.
- S. W. Hawking, I. G. Moss, and J. M. Stewart, Bubble collisions in the very early universe, Phys. Rev. D 26, 2681 (1982).
- B. Carr, K. Kohri, Y. Sendouda, and J. Yokoyama, Constraints on primordial black holes, Rep. Prog. Phys. 84, 116902 (2021).
- Y. Xiao, J. M. Yang, and Y. Zhang, Dilution of dark matter relic density in singlet extension models, J. High Energy Phys. 02 (2023) 008.
- Y. Xiao, J. M. Yang, and Y. Zhang, Implications of nano-Hertz gravitational waves on electroweak phase transition in the singlet dark matter model, Sci. Bull. 68, 3158 (2023).
- A. D. Linde, Decay of the false vacuum at finite temperature, Nucl. Phys. B216, 421 (1983).
- S. R. Coleman, The fate of the false vacuum. 1. Semiclassical theory, Phys. Rev. D 15, 2929 (1977).
- M. Gleiser, E. W. Kolb, and R. Watkins, Phase transitions with subcritical bubbles, Nucl. Phys. B364, 411 (1991).
- M. Gleiser and E. W. Kolb, Fluctuation driven electroweak phase transition, Phys. Rev. Lett. 69, 1304 (1992).
- G. W. Anderson, Collapsing subcritical bubbles, Phys. Lett. B 295, 32 (1992).
- G. Gelmini and M. Gleiser, Kinetics of subcritical bubbles and the electroweak transition, Nucl. Phys. B419, 129 (1994).
- T. Shiromizu, M. Morikawa, and J. Yokoyama, Dynamics of subcritical bubbles in first order phase transition, Prog. Theor. Phys. 94, 805 (1995).
- M. Gleiser, A. F. Heckler, and E. W. Kolb, Modeling thermal fluctuations: Phase mixing and percolation, Phys. Lett. B 405, 121 (1997).
- J. Borrill and M. Gleiser, Thermal phase mixing during first order phase transitions, Phys. Rev. D 51, 4111 (1995).
- L. Bian, G. Chen, S. Li, H. Wang, Y. Xiao, J. M. Yang et al., Gravitational wave signature of aspherical bubbles driven by thermal fluctuation, arXiv:2601.15933.
- V. Rubakov, Classical theory of gauge fields, in Classical Theory of Gauge Fields (Princeton University Press, Princeton, NJ, 2009).
- M. Quiros, Finite temperature field theory and phase transitions, in Proceedings of the, Summer school in high-energy physics and cosmology: Trieste, Italy 1999 (World Scientific, Singapore, 1998), p. 187.
- A. Ekstedt, O. Gould, and J. Hirvonen, BubbleDet: A python package to compute functional determinants for bubble nucleation, J. High Energy Phys. 12 (2023) 056.
- C. L. Wainwright, cosmotransitions: Computing cosmological phase transition temperatures and bubble profiles with multiple fields, Comput. Phys. Commun. 183, 2006 (2012).