- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Inverse bubbles from broken supersymmetry

Giulio Barni1,*, Simone Blasi2,†, and Miguel Vanvlasselaer3,‡

  • *Contact author: giulio.barni@ift.csic.es
  • †Contact author: simone.blasi@desy.de
  • ‡Contact author: miguel.vanvlasselaer@vub.be
PDF

Phys. Rev. D 112, 095006 – Published 7 November, 2025

DOI: https://doi.org/10.1103/pmf7-vlvc

Abstract

Building upon the recent findings regarding inverse phase transitions in the early Universe, we present the first natural realization of this phenomenon within a supersymmetry-breaking sector. We demonstrate that inverse hydrodynamics, which is characterized by the fluid being sucked by the bubble wall rather than being pushed or dragged, is actually not limited to a phase of (re)heating but can also occur within the standard cooling cosmology. Through a numerical analysis of the phase transition, we establish a simple and generic criterion to determine its hydrodynamics based on the generalized pseudotrace. Our results provide a proof of principle highlighting the need to account for these new fluid solutions when considering cosmological phase transitions and their phenomenological implications.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (115)

  1. V. A. Kuzmin, V. A. Rubakov, and M. E. Shaposhnikov, On the anomalous electroweak baryon number nonconservation in the early Universe, Phys. Lett. 155B, 36 (1985).
  2. M. Shaposhnikov, Possible appearance of the baryon asymmetry of the Universe in an electroweak theory, JETP Lett. 44, 465 (1986), https://inspirehep.net/literature/241033.
  3. A. E. Nelson, D. B. Kaplan, and A. G. Cohen, Why there is something rather than nothing: Matter from weak interactions, Nucl. Phys. B373, 453 (1992).
  4. M. Carena, M. Quiros, and C. E. M. Wagner, Opening the window for electroweak baryogenesis, Phys. Lett. B 380, 81 (1996).
  5. J. M. Cline, Is electroweak baryogenesis dead?, Phil. Trans. R. Soc. A 376, 20170116 (2018).
  6. A. J. Long, A. Tesi, and L.-T. Wang, Baryogenesis at a lepton-number-breaking phase transition, J. High Energy Phys. 10 (2017) 095.
  7. S. Bruggisser, B. Von Harling, O. Matsedonskyi, and G. Servant, Electroweak phase transition and baryogenesis in composite Higgs models, J. High Energy Phys. 12 (2018) 099.
  8. S. Bruggisser, B. Von Harling, O. Matsedonskyi, and G. Servant, Baryon asymmetry from a composite Higgs boson, Phys. Rev. Lett. 121, 131801 (2018).
  9. S. Bruggisser, B. von Harling, O. Matsedonskyi, and G. Servant, Status of electroweak baryogenesis in minimal composite Higgs, J. High Energy Phys. 08 (2023) 012.
  10. D. E. Morrissey and M. J. Ramsey-Musolf, Electroweak baryogenesis, New J. Phys. 14, 125003 (2012).
  11. A. Azatov, M. Vanvlasselaer, and W. Yin, Baryogenesis via relativistic bubble walls, J. High Energy Phys. 10 (2021) 043.
  12. P. Huang and K.-P. Xie, Leptogenesis triggered by a first-order phase transition, J. High Energy Phys. 09 (2022) 052.
  13. I. Baldes, S. Blasi, A. Mariotti, A. Sevrin, and K. Turbang, Baryogenesis via relativistic bubble expansion, Phys. Rev. D 104, 115029 (2021).
  14. E. J. Chun, T. P. Dutka, T. H. Jung, X. Nagels, and M. Vanvlasselaer, Bubble-assisted leptogenesis, J. High Energy Phys. 09 (2023) 164.
  15. A. Falkowski and J. M. No, Non-thermal dark matter production from the electroweak phase transition: Multi-TeV WIMPs and ’Baby-Zillas’, J. High Energy Phys. 02 (2013) 034.
  16. I. Baldes, Y. Gouttenoire, and F. Sala, String fragmentation in supercooled confinement and implications for dark matter, J. High Energy Phys. 04 (2021) 278.
  17. J.-P. Hong, S. Jung, and K.-P. Xie, Fermi-ball dark matter from a first-order phase transition, Phys. Rev. D 102, 075028 (2020).
  18. A. Azatov, M. Vanvlasselaer, and W. Yin, Dark matter production from relativistic bubble walls, J. High Energy Phys. 03 (2021) 288.
  19. I. Baldes, Y. Gouttenoire, F. Sala, and G. Servant, Supercool composite dark matter beyond 100 TeV, J. High Energy Phys. 07 (2022) 084.
  20. P. Asadi, E. D. Kramer, E. Kuflik, G. W. Ridgway, T. R. Slatyer, and J. Smirnov, Thermal squeezeout of dark matter, Phys. Rev. D 104, 095013 (2021).
  21. P. Lu, K. Kawana, and K.-P. Xie, Old phase remnants in first-order phase transitions, Phys. Rev. D 105, 123503 (2022).
  22. I. Baldes, Y. Gouttenoire, and F. Sala, Hot and heavy dark matter from a weak scale phase transition, SciPost Phys. 14, 033 (2023).
  23. A. Azatov, G. Barni, S. Chakraborty, M. Vanvlasselaer, and W. Yin, Ultra-relativistic bubbles from the simplest Higgs portal and their cosmological consequences, J. High Energy Phys. 10 (2022) 017.
  24. I. Baldes, M. Dichtl, Y. Gouttenoire, and F. Sala, Bubbletrons, Phys. Rev. Lett. 134, 061001 (2025).
  25. M. Kierkla, A. Karam, and B. Swiezewska, Conformal model for gravitational waves and dark matter: A status update, J. High Energy Phys. 03 (2023) 007.
  26. G. F. Giudice, H. M. Lee, A. Pomarol, and B. Shakya, Nonthermal heavy dark matter from a first-order phase transition, J. High Energy Phys. 12 (2024) 190.
  27. A. Azatov, X. Nagels, M. Vanvlasselaer, and W. Yin, Populating secluded dark sector with ultra-relativistic bubbles, J. High Energy Phys. 11 (2024) 129.
  28. H. Kodama, M. Sasaki, and K. Sato, Abundance of primordial holes produced by cosmological first order phase transition, Prog. Theor. Phys. 68, 1979 (1982).
  29. K. Kawana and K.-P. Xie, Primordial black holes from a cosmic phase transition: The collapse of Fermi-balls, Phys. Lett. B 824 (2022) 136791,
  30. T. H. Jung and T. Okui, Primordial black holes from bubble collisions during a first-order phase transition, Phys. Rev. D 110, 115014 (2024).
  31. Y. Gouttenoire and T. Volansky, Primordial black holes from supercooled phase transitions, Phys. Rev. D 110, 043514 (2024).
  32. M. Lewicki, P. Toczek, and V. Vaskonen, Primordial black holes from strong first-order phase transitions, J. High Energy Phys. 09 (2023) 092.
  33. E. Witten, Cosmic separation of phases, Phys. Rev. D 30, 272 (1984).
  34. C. J. Hogan, Gravitational radiation from cosmological phase transitions, Mon. Not. R. Astron. Soc. 218, 629 (1986).
  35. A. Kosowsky and M. S. Turner, Gravitational radiation from colliding vacuum bubbles: Envelope approximation to many bubble collisions, Phys. Rev. D 47, 4372 (1993).
  36. A. Kosowsky, M. S. Turner, and R. Watkins, Gravitational waves from first order cosmological phase transitions, Phys. Rev. Lett. 69, 2026 (1992).
  37. M. Kamionkowski, A. Kosowsky, and M. S. Turner, Gravitational radiation from first order phase transitions, Phys. Rev. D 49, 2837 (1994).
  38. A. Romero, K. Martinovic, T. A. Callister, H.-K. Guo, M. Martínez, M. Sakellariadou, F.-W. Yang, and Y. Zhao, Implications for first-order cosmological phase transitions from the third LIGO-Virgo observing run, Phys. Rev. Lett. 126, 151301 (2021).
  39. T. Bringmann, P. F. Depta, T. Konstandin, K. Schmidt-Hoberg, and C. Tasillo, Does NANOGrav observe a dark sector phase transition?, J. Cosmol. Astropart. Phys. 11 (2023) 053.
  40. C. Caprini et al., Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions, J. Cosmol. Astropart. Phys. 04 (2016) 001.
  41. M. Maggiore et al. (ET Collaboration), Science case for the Einstein telescope, J. Cosmol. Astropart. Phys. 03 (2020) 050.
  42. R. Pasechnik, M. Reichert, F. Sannino, and Z.-W. Wang, Gravitational waves from composite dark sectors, J. High Energy Phys. 02 (2024) 159.
  43. A. Azatov and M. Vanvlasselaer, Phase transitions in perturbative walking dynamics, J. High Energy Phys. 09 (2020) 085.
  44. M. T. Frandsen, M. Heikinheimo, M. Rosenlyst, M. E. Thing, and K. Tuominen, Gravitational waves from SU(N)/SP(N) composite Higgs models, J. High Energy Phys. 09 (2023) 022.
  45. M. Reichert and Z.-W. Wang, Gravitational waves from dark composite dynamics, EPJ Web Conf. 274, 08003 (2022).
  46. K. Fujikura, Y. Nakai, R. Sato, and Y. Wang, Cosmological phase transitions in composite Higgs models, J. High Energy Phys. 09 (2023) 053.
  47. C. Delaunay, C. Grojean, and J. D. Wells, Dynamics of non-renormalizable electroweak symmetry breaking, J. High Energy Phys. 04 (2008) 029.
  48. G. Kurup and M. Perelstein, Dynamics of electroweak phase transition in singlet-scalar extension of the standard model, Phys. Rev. D 96, 015036 (2017).
  49. B. von Harling and G. Servant, QCD-induced electroweak phase transition, J. High Energy Phys. 01 (2018) 159.
  50. A. Azatov, D. Barducci, and F. Sgarlata, Gravitational traces of broken gauge symmetries, J. Cosmol. Astropart. Phys. 07 (2020) 027.
  51. T. Ghosh, H.-K. Guo, T. Han, and H. Liu, Electroweak phase transition with an SU(2) dark sector, J. High Energy Phys. 07 (2021) 045.
  52. M. Aoki, T. Komatsu, and H. Shibuya, Possibility of a multi-step electroweak phase transition in the two-Higgs doublet models, Prog. Theor. Exp. Phys. 2022, 063B05 (2022).
  53. M. Badziak and I. Nalecz, First-order phase transitions in twin Higgs models, J. High Energy Phys. 02 (2023) 185.
  54. U. Banerjee, S. Chakraborty, S. Prakash, and S. U. Rahaman, The feasibility of ultra-relativistic bubbles in SMEFT, Phys. Rev. D 110, 055002 (2024).
  55. L. Delle Rose, G. Panico, M. Redi, and A. Tesi, Gravitational waves from supercool axions, J. High Energy Phys. 04 (2020) 025.
  56. B. Von Harling, A. Pomarol, O. Pujolàs, and F. Rompineve, Peccei-Quinn phase transition at LIGO, J. High Energy Phys. 04 (2020) 195.
  57. J. Halverson, C. Long, A. Maiti, B. Nelson, and G. Salinas, Gravitational waves from dark Yang-Mills sectors, J. High Energy Phys. 05 (2021) 154.
  58. E. Morgante, N. Ramberg, and P. Schwaller, Gravitational waves from dark SU(3) Yang-Mills theory, Phys. Rev. D 107, 036010 (2023).
  59. R. Jinno and M. Takimoto, Probing a classically conformal B-L model with gravitational waves, Phys. Rev. D 95, 015020 (2017).
  60. A. Addazi, A. Marcianò, A. P. Morais, R. Pasechnik, J. a. Viana, and H. Yang, Gravitational echoes of lepton number symmetry breaking with light and ultralight Majorons, J. Cosmol. Astropart. Phys. 09 (2023) 026; 03 (2024) E01.
  61. N. J. Craig, Gravitational waves from supersymmetry breaking, arXiv:0902.1990.
  62. N. Craig, N. Levi, A. Mariotti, and D. Redigolo, Ripples in spacetime from broken supersymmetry, J. High Energy Phys. 21 (2020) 184.
  63. P. J. Steinhardt, Monopole and vortex dissociation and decay of the false vacuum, Nucl. Phys. B190, 583 (1981).
  64. Y. Hosotani, Impurities in the early Universe, Phys. Rev. D 27, 789 (1983).
  65. U. A. Yajnik, Phase transition induced by cosmic strings, Phys. Rev. D 34, 1237 (1986).
  66. K. Mukaida and M. Yamada, False vacuum decay catalyzed by black holes, Phys. Rev. D 96, 103514 (2017).
  67. D. Canko, I. Gialamas, G. Jelic-Cizmek, A. Riotto, and N. Tetradis, On the catalysis of the electroweak vacuum decay by black holes at high temperature, Eur. Phys. J. C 78, 328 (2018).
  68. R. Jinno, T. Konstandin, H. Rubira, and J. van de Vis, Effect of density fluctuations on gravitational wave production in first-order phase transitions, J. Cosmol. Astropart. Phys. 12 (2021) 019.
  69. R. Balkin, J. Serra, K. Springmann, S. Stelzl, and A. Weiler, Density induced vacuum instability, SciPost Phys. 14, 071 (2023).
  70. P. Agrawal and M. Nee, The boring monopole, SciPost Phys. 13, 049 (2022).
  71. S. Blasi and A. Mariotti, Domain walls seeding the electroweak phase transition, Phys. Rev. Lett. 129, 261303 (2022).
  72. P. Agrawal, S. Blasi, A. Mariotti, and M. Nee, Electroweak phase transition with a double well done doubly well, J. High Energy Phys. 06 (2024) 089.
  73. R. Jinno, J. Kume, and M. Yamada, Super-slow phase transition catalyzed by BHs and the birth of baby BHs, Phys. Lett. B 849, 138465 (2024).
  74. S. Blasi and A. Mariotti, QCD axion strings or seeds?, SciPost Phys. 18, 016 (2025).
  75. S. Blasi, R. Jinno, T. Konstandin, H. Rubira, and I. Stomberg, Gravitational waves from defect-driven phase transitions: Domain walls, J. Cosmol. Astropart. Phys. 10 (2023) 051.
  76. R. Balkin, J. Serra, K. Springmann, S. Stelzl, and A. Weiler, Runaway relaxion from finite density, J. High Energy Phys. 06 (2022) 023.
  77. J. Casalderrey-Solana, D. Mateos, and M. Sanchez-Garitaonandia, Mega-hertz gravitational waves from neutron star mergers, arXiv:2210.03171.
  78. R. Balkin, J. Serra, K. Springmann, S. Stelzl, and A. Weiler, Heavy neutron stars from light scalars, J. High Energy Phys. 02 (2025) 141.
  79. M. Laine, Bubble growth as a detonation, Phys. Rev. D 49, 3847 (1994).
  80. H. Kurki-Suonio and M. Laine, Supersonic deflagrations in cosmological phase transitions, Phys. Rev. D 51, 5431 (1995).
  81. M. Laine and K. Rummukainen, What’s new with the electroweak phase transition?, Nucl. Phys. B, Proc. Suppl. 73, 180 (1999).
  82. J. R. Espinosa, T. Konstandin, J. M. No, and G. Servant, Energy budget of cosmological first-order phase transitions, J. Cosmol. Astropart. Phys. 06 (2010) 028.

  83. The plasma frame is defined as the frame in which the center of the bubble is at rest.

  84. G. Barni, S. Blasi, and M. Vanvlasselaer, The hydrodynamics of inverse phase transitions, J. Cosmol. Astropart. Phys. 10 (2024) 042.
  85. Y. Bea, J. Casalderrey-Solana, D. Mateos, and M. Sanchez-Garitaonandia, Hydrodynamics of relativistic superheated bubbles, arXiv:2406.14450.
  86. D. Cutting, E. Vilhonen, and D. J. Weir, Droplet collapse during strongly supercooled transitions, Phys. Rev. D 106, 103524 (2022).
  87. M. A. Buen-Abad, J. H. Chang, and A. Hook, Gravitational wave signatures from reheating, Phys. Rev. D 108, 036006 (2023).
  88. C. Caprini and J. M. No, Supersonic electroweak baryogenesis: Achieving baryogenesis for fast bubble walls, J. Cosmol. Astropart. Phys. 01 (2012) 031.
  89. J. B. Dent, B. Dutta, and M. Rai, Imprints of early Universe cosmology on gravitational waves, J. High Energy Phys. 03 (2025) 098.
  90. L. O’Raifeartaigh, Spontaneous symmetry breaking for chiral scalar superfields, Nucl. Phys. B96, 331 (1975).
  91. A. E. Nelson and N. Seiberg, R symmetry breaking versus supersymmetry breaking, Nucl. Phys. B416, 46 (1994).
  92. K. A. Intriligator, N. Seiberg, and D. Shih, Supersymmetry breaking, R-symmetry breaking and metastable vacua, J. High Energy Phys. 07 (2007) 017.
  93. N. J. Craig, P. J. Fox, and J. G. Wacker, Reheating metastable o’raifeartaigh models, Phys. Rev. D 75, 085006 (2007).
  94. A. Katz, On the thermal history of calculable gauge mediation, J. High Energy Phys. 10 (2009) 054.
  95. See Supplemental Material at http://link.aps.org/supplemental/10.1103/pmf7-vlvc for further details on the derivation of the effective potential and other thermodynamical quantities.
  96. S. Coleman and E. Weinberg, Radiative corrections as the origin of spontaneous symmetry breaking, Phys. Rev. D 7, 1888 (1973).
  97. M. Quiros, Finite temperature field theory and phase transitions, in ICTP Summer School in High-Energy Physics and Cosmology (1999), 1, pp. 187–259, .
  98. D. Curtin, P. Meade, and H. Ramani, Thermal resummation and phase transitions, Eur. Phys. J. C 78, 787 (2018).

  99. We remind the reader that the velocities v± have to be understood in the front frame, where the bubble wall is at rest.

  100. F. Giese, T. Konstandin, and J. van de Vis, Model-independent energy budget of cosmological first-order phase transitions—A sound argument to go beyond the bag model, J. Cosmol. Astropart. Phys. 07 (2020) 057.
  101. L. Leitao and A. Megevand, Hydrodynamics of phase transition fronts and the speed of sound in the plasma, Nucl. Phys. B891, 159 (2015).
  102. S. R. Coleman, The fate of the false vacuum. 1. Semiclassical theory, Phys. Rev. D 15, 2929 (1977). 16, 1248(E) (1977).
  103. A. D. Linde, Fate of the false vacuum at finite temperature: Theory and applications, Phys. Lett. 100B, 37 (1981).
  104. A. D. Linde, Decay of the false vacuum at finite temperature, Nucl. Phys. B216, 421 (1983). B223, 544(E) (1983).
  105. J. Ellis, M. Lewicki, J. M. No, and V. Vaskonen, Gravitational wave energy budget in strongly supercooled phase transitions, J. Cosmol. Astropart. Phys. 06 (2019) 024.
  106. A. H. Guth and S. H. H. Tye, Phase transitions and magnetic monopole production in the very early Universe, Phys. Rev. Lett. 44, 963 (1980).
  107. K. Enqvist, J. Ignatius, K. Kajantie, and K. Rummukainen, Nucleation and bubble growth in a first order cosmological electroweak phase transition, Phys. Rev. D 45, 3415 (1992).

  108. The relation Tnuc=T+ only holds for detonations and antideflagrations. For the other expansion modes, we still use this as a sensible approximation to identify the relevant v± branch.

  109. Y. Bea, M. Giliberti, D. Mateos, M. Sanchez-Garitaonandia, A. Serantes, and M. Zilhão, Bubble dynamics in a QCD-like phase diagram, arXiv:2412.09588.
  110. W.-Y. Ai, B. Laurent, and J. van de Vis, Model-independent bubble wall velocities in local thermal equilibrium, J. Cosmol. Astropart. Phys. 07 (2023) 002.
  111. W.-Y. Ai, B. Laurent, and J. van de Vis, Bounds on the bubble wall velocity, J. High Energy Phys. 02 (2025) 119.
  112. W.-Y. Ai, X. Nagels, and M. Vanvlasselaer, Criterion for ultra-fast bubble walls: The impact of hydrodynamic obstruction, J. Cosmol. Astropart. Phys. 03 (2024) 037.

  113. A spectator field does not change its physical properties, e.g., its mass, during the phase transition.

  114. F. Giese, T. Konstandin, K. Schmitz, and J. van de Vis, Model-independent energy budget for LISA, J. Cosmol. Astropart. Phys. 01 (2021) 072.
  115. M. Sanchez-Garitaonandia and J. van de Vis, Prediction of the bubble wall velocity for a large jump in degrees of freedom, Phys. Rev. D 110, 023509 (2024).

Outline

Information

Phys. Rev. D 112, 095006– Published 7 November, 2025
  • Received 17 March 2025
  • Revised 11 June 2025
  • Accepted 15 October 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation