- 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

Matter sourced bubble nucleation in the asymmetron scalar-tensor theory

Usama Syed Aqeel, Clare Burrage, Oliver Gould, and Paul M. Saffin

  • Centre for Astronomy and Particle Theory, The School of Physics and Astronomy, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom

PDF

Phys. Rev. D 113, 056022 – Published 25 March, 2026

DOI: https://doi.org/10.1103/z9gn-q74p

Abstract

We investigate how matter density distributions affect thin-wall bubble formation in the asymmetron mechanism, a scalar–tensor theory with a universal coupling to matter and explicit symmetry breaking, and analyze the stability of its metastable state. We show that the screening mechanism of the asymmetron inside dense objects induces a surface tension associated with the boundary of the screening object, leading to a richer class of bubble solutions than the standard Coleman-Callan bulk nucleation. These boundary surface tensions are used to modify the Nambu-Goto action for instantons, allowing for the computation of the corresponding Euclidean action for bubbles nucleating on flat planes, as well as on concave and convex cylindrical surfaces. We find that the smallest Euclidean action occurs for bubbles nucleating along the edge of a concave spherical surface. Comparing this edge nucleation channel with the bulk one, we determine the maximum curvature radius for which concave edge nucleation is preferred. Since the maximum radius of curvature is exponentially suppressed by the action of a bulk bubble, we find that within the regime of the instanton approximation, edge nucleation is always preferred. This is largely due to the weak couplings of the asymmetron. We apply these findings to determine the maximum curvature radius of a cosmic void and discuss how our results affect the seeding of N-body simulations of asymmetron domains, showing that domain wall nucleation preferentially occurs at the edges of cosmological voids. We also demonstrate that the presence of a homogeneous gas around the dense substrates reduces the maximum curvature radius, enabling bulk bubbles to form preferentially as the asymmetron undergoes a density-driven phase transition.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (66)

  1. A. Mazumdar and G. White, Review of cosmic phase transitions: Their significance and experimental signatures, Rep. Prog. Phys. 82, 076901 (2019).
  2. S. Coleman, Fate of the false vacuum: Semiclassical theory, Phys. Rev. D 15, 2929 (1977).
  3. C. G. Callan and S. Coleman, Fate of the false vacuum. II. First quantum corrections, Phys. Rev. D 16, 1762 (1977).
  4. S. Coleman and F. De Luccia, Gravitational effects on and of vacuum decay, Phys. Rev. D 21, 3305 (1980).
  5. I. Affleck, Quantum-statistical metastability, Phys. Rev. Lett. 46, 388 (1981).
  6. A. H. Guth, Inflationary universe: A possible solution to the horizon and flatness problems, Phys. Rev. D 23, 347 (1981).
  7. A. Linde, Chaotic inflation, Phys. Lett. 129B, 177 (1983).
  8. V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberger, Theory of cosmological perturbations, Phys. Rep. 215, 203 (1992).
  9. M. Paranjape, The Theory and Applications of Instanton Calculations (Oxford University Press, New York, 2018).
  10. S. Coleman, Aspects of Symmetry: Selected Erice Lectures (Cambridge University Press, Cambridge, England, 1985).
  11. K. Hinterbichler and J. Khoury, Screening long-range forces through local symmetry restoration, Phys. Rev. Lett. 104, 231301 (2010).
  12. K. Hinterbichler, J. Khoury, A. Levy, and A. Matas, Symmetron cosmology, Phys. Rev. D 84, 103521 (2011).
  13. A. Vilenkin and E. Shellard, Cosmic Strings and Other Topological Defects, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 1994).
  14. T. Vachaspati, Kinks and Domain Walls: An Introduction to Classical and Quantum Solitons (Oxford University Press, New York, 2007).
  15. M. Abdul Karim, J. Aguilar, S. Ahlen, S. Alam, L. Allen, C. Allende Prieto, O. Alves, A. Anand, U. Andrade et al., DESI DR2 II: Measurements of baryon acoustic oscillations and cosmological constraints, Phys. Rev. D 112, 083515 (2025).
  16. L. Perivolaropoulos and F. Skara, Gravitational transitions via the explicitly broken symmetron screening mechanism, Phys. Rev. D 106, 043528 (2022).
  17. O. Christiansen, F. Hassani, M. Jalilvand, and D. F. Mota, Asevolution: A relativistic n-body implementation of the (a)symmetron, J. Cosmol. Astropart. Phys. 05 (2023) 009.
  18. P. Chen, T. Suyama, and J. Yokoyama, Spontaneous-scalarization-induced dark matter and variation of the gravitational constant, Phys. Rev. D 92, 124016 (2015).
  19. J. Langer, Statistical theory of the decay of metastable states, Ann. Phys. (N.Y.) 54, 258 (1969).
  20. J. Langer, Theory of the condensation point, Ann. Phys. (N.Y.) 41, 108 (1967).
  21. F. Devoto, S. Devoto, L. Di Luzio, and G. Ridolfi, False vacuum decay: An introductory review, J. Phys. G 49, 103001 (2022).
  22. M. Canaletti and I. G. Moss, Seeding the decay of the false vacuum, Phys. Rev. D 110, 105015 (2024).
  23. A. C. Jenkins, H. V. Peiris, and A. Pontzen, Bubbles in a box: Eliminating edge nucleation in cold-atom simulators of vacuum decay, Phys. Rev. A 112, 023318 (2025).
  24. K. Brown, I. G. Moss, and T. P. Billam, Mitigating boundary effects in finite temperature simulations of false vacuum decay, arXiv:2504.03509.
  25. I. G. Moss, Black-hole bubbles, Phys. Rev. D 32, 1333 (1985).
  26. R. Gregory, I. G. Moss, and B. Withers, Black holes as bubble nucleation sites, J. High Energy Phys. 03 (2014) 081.
  27. R. Gregory, I. G. Moss, N. Oshita, and S. Patrick, Hawking-moss transition with a black hole seed, J. High Energy Phys. 09 (2020) 135.
  28. A. Shkerin and S. Sibiryakov, Black hole induced false vacuum decay from first principles, J. High Energy Phys. 11 (2021) 197.
  29. A. R. Brown and E. J. Weinberg, Thermal derivation of the coleman-de luccia tunneling prescription, Phys. Rev. D 76, 064003 (2007).
  30. G. W. Gibbons and S. W. Hawking, Cosmological event horizons, thermodynamics, and particle creation, Phys. Rev. D 15, 2738 (1977).
  31. R. Bousso and S. W. Hawking, (Anti-)evaporation of Schwarzschild–de sitter black holes, Phys. Rev. D 57, 2436 (1998).
  32. C. Llinares and P. Brax, Detecting coupled domain walls in laboratory experiments, Phys. Rev. Lett. 122, 091102 (2019).
  33. K. Clements, B. Elder, L. Hackermueller, M. Fromhold, and C. Burrage, Detecting dark domain walls, Phys. Rev. D 109, 123023 (2024).
  34. A. Joyce, B. Jain, J. Khoury, and M. Trodden, Beyond the cosmological standard model, Phys. Rep. 568, 1 (2015).
  35. T. Clifton, P. G. Ferreira, A. Padilla, and C. Skordis, Modified gravity and cosmology, Phys. Rep. 513, 1 (2012).
  36. C. Burrage, B. Elder, P. Millington, D. Saadeh, and B. Thrussell, Fifth-force screening around extremely compact sources, J. Cosmol. Astropart. Phys. 08 (2021) 052.
  37. E. B. Bogomolny, Stability of classical solutions, Sov. J. Nucl. Phys. 24, 449 (1976).
  38. P. Brax, S. Casas, H. Desmond, and B. Elder, Testing screened modified gravity, Universe 8, 11 (2021).
  39. C. D. Panda, M. J. Tao, M. Ceja, J. Khoury, G. M. Tino, and H. Müller, Measuring gravitational attraction with a lattice atom interferometer, Nature (London) 631, 515 (2024).
  40. H. Fischer, C. Käding, and M. Pitschmann, Screened scalar fields in the laboratory and the solar system, Universe 10, 297 (2024).
  41. M. Högås and E. Mörtsell, Impact of symmetron screening on the Hubble tension: New constraints using cosmic distance ladder data, Phys. Rev. D 108, 024007 (2023).
  42. A. Eichhorn, H. Gies, J. Jaeckel, T. Plehn, M. M. Scherer, and R. Sondenheimer, The Higgs mass and the scale of new physics, J. High Energy Phys. 04 (2015) 022.
  43. V. Branchina and E. Messina, Stability and UV completion of the standard model, Europhys. Lett. 117, 61002 (2017).
  44. H. Gies and R. Sodenheimer, Renormalization group flow of the Higgs potential, Phil. Trans. R. Soc. A 376, 20170120 (2018).
  45. M. Udemba and P. Millington, Quantum corrections to symmetron fifth-force profiles, arXiv:2508.16726.
  46. U. S. Aqeel and A. Rajantie, Gravitational aspects of false vacuum decay, Master’s thesis, Imperial College London, 2022.
  47. C. L. Wainwright, Cosmotransitions: Computing cosmological phase transition temperatures and bubble profiles with multiple fields, Comput. Phys. Commun. 183, 2006 (2012).
  48. M. Matteini, M. Nemevšek, and L. Ubaldi, Analytic false-vacuum decay rate in the thin-wall approximation, Proc. Sci. CORFU2022 (2023) 116 [arXiv:2304.02290].
  49. A. Mégevand and F. A. Membiela, Thin and thick bubble walls. Part I. Vacuum phase transitions, J. Cosmol. Astropart. Phys. 06 (2023) 007.
  50. A. Mégevand and F. A. Membiela, Thin and thick bubble walls II: Expansion in the wall width, J. Cosmol. Astropart. Phys. 04 (2024) 003.
  51. A. Mégevand and F. A. Membiela, Thin and thick bubble walls III: Wall energy, J. Cosmol. Astropart. Phys. 05 (2025) 076.
  52. J. Garriga, Instantons for vacuum decay at finite temperature in the thin wall limit, Phys. Rev. D 49, 5497 (1994).
  53. M. Soleimani, R. J. Hill, and T. G. M. van de Ven, Bubbles and drops on curved surfaces, Langmuir 29, 14168 (2013).
  54. A. Pressley, Elementary Differential Geometry (Springer, New York, 2001).
  55. B. F. de Aguiar, R. F. P. Mendes, and F. T. Falciano, Neutron stars in the symmetron model, Universe 8, 6 (2021).
  56. J. Ignatius, Bubble free energy in cosmological phase transitions, Phys. Lett. B 309, 252 (1993).
  57. H. Widyan and M. Al-Wardat, Classical solution for the bounce up to second order, Chin. J. Phys. (Taipei) 48, 736 (2010).
  58. K. Kajantie, J. Potvin, and K. Rummukainen, Curvature effects on the free energy of QCD bubbles, Preprint (1992).
  59. O. Gould and J. Hirvonen, Effective field theory approach to thermal bubble nucleation, Phys. Rev. D 104, 096015 (2021).
  60. J. Garriga, Nucleation rates in flat and curved space, Phys. Rev. D 49, 6327 (1994).
  61. C. G. Callan and J. Maldacena, Brane dynamics from the Born-Infeld action, Nucl. Phys. B513, 198 (1998).
  62. 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.
  63. A. Bhattacharya, J. Cotler, A. Dersy, and M. D. Schwartz, Collective coordinate fix in the path integral, Phys. Rev. D 110, 116023 (2024).
  64. O. Gould and A. Rajantie, Thermal Schwinger pair production at arbitrary coupling, Phys. Rev. D 96, 076002 (2017).
  65. U. S. Aqeel, asymmetron-bubbles, version 1.0, https://github.com/usama-bit137/asymmetron-bubbles (2025).
  66. E. W. Kolb and M. S. Turner, The Early Universe (Taylor and Francis, London, 2019), Vol. 69.

Outline

Information

Phys. Rev. D 113, 056022– Published 25 March, 2026
  • Received 21 November 2025
  • Accepted 9 February 2026
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