Probing Beyond the Standard Model with Gravitational Waves from Phase Transitions

Chiara Caprini

doi:10.53941/hihep.2025.100022

Abstract

This review article is based on a seminar presented at the Higgs pairs workshop 2025. Stochastic gravitational wave backgrounds can serve as probe of the diverse phenomenology encountered in beyond-Standard-Model scenarios featuring phase transitions in the early Universe. Focussing on gravitational wave production from first-order phase transitions, we present the main results of a recent analysis by the LISA Cosmology Working Group concerning the detectability of such signals with LISA. Strong degeneracies, both among the parameters controlling the phase transition and between these and the parameters of the beyond-Standard-Model scenario underlying the phase transition, complicate the reconstruction of the model from a potential signal. Nonetheless, once a specific scenario is assumed, LISA observations can supply constraints possibly complementary to those obtainable from present and future particle colliders.

References

1.
Maggiore, M. Gravitational wave experiments and early universe cosmology. Phys. Rep. 2000, 331, 283–367.
2.
Durrer, R. The Cosmic Microwave Background; Cambridge University Press: Cambridge, UK, 2020.
3.
Caprini, C.; Figueroa, D.G. Cosmological Backgrounds of Gravitational Waves. Class. Quant. Grav. 2018, 35, 163001.
4.
Maggiore, M. Gravitational Waves: Astrophysics and Cosmology; Oxford University Press: Oxford, UK, 2018; Volume 2.
5.
Athron, P.; Balazs, C.; Fowlie, A.; et al. Cosmological phase transitions: From perturbative particle physics to gravitational waves. Prog. Part. Nucl. Phys. 2024, 135, 104094.
6.
Romano, J.D.; Cornish, N.J. Detection methods for stochastic gravitational-wave backgrounds: A unified treatment. Living Rev. Rel. 2017, 20, 2.
7.
Colpi, M.; Danzmann, K.; Hewitson, M.; et al. LISA Definition Study Report. arXiv 2024, arXiv:2402.07571.
8.
Baghi, Q.; Karnesis, N.; Bayle, J.B.; et al. Uncovering gravitational-wave backgrounds from noises of unknown shape with LISA. J. Cosmol. Astropart. Phys. 2023, 2023, 066.
9.
Karnesis, N.; Lilley, M.; Petiteau, A. Assessing the detectability of a Stochastic Gravitational Wave Background with LISA, using an excess of power approach. Class. Quant. Grav. 2020, 37, 215017.
10.
Santini, A.; Muratore, M.; Gair, J.; et al. Flexible, GPU-accelerated approach for the joint characterization of LISA instrumental noise and stochastic gravitational wave backgrounds. Phys. Rev. D 2025, 112, 084050.
11.
Pozzoli, F.; Gair, J.; Buscicchio, R.; et al. Is the stochastic signal really detectable? Phys. Rev. D 2025, 112, 064035.
12.
Boileau, G.; Christensen, N.; Gowling, C.; et al. Prospects for LISA to detect a gravitational-wave background from first order phase transitions. J. Cosmol. Astropart. Phys. 2023, 02, 056.
13.
Hindmarsh, M.; Hooper, D.C.; Minkkinen, T.; et al. Recovering a phase transition signal in simulated LISA data with a modulated galactic foreground. J. Cosmol. Astropart. Phys. 2025, 2025, 052.
14.
Caprini, C.; Pujol`as, O.; Quelquejay-Leclere, H.; et al. Primordial gravitational wave backgrounds from phase transitions with next generation ground based detectors. Class. Quant. Grav. 2025, 42, 045015.
15.
Caprini, C.; Jinno, R.; Lewicki, M.; et al. Gravitational waves from first-order phase transitions in LISA: reconstruction pipeline and physics interpretation. J. Cosmol. Astropart. Phys. 2024, 2024, 020.
16.
Bartolo, N.; Bertacca, D.; Caldwell, R.; et al. Probing anisotropies of the Stochastic Gravitational Wave Background with LISA. J. Cosmol. Astropart. Phys. 2022, 2022, 009.
17.
Available online: https://www.ligo.caltech.edu/ (accessed on 10 November 2025).
18.
Available online: https://www.virgo-gw.eu/ (accessed on 10 November 2025).
19.
Available online: https://gwcenter.icrr.u-tokyo.ac.jp/en/ (accessed on 10 November 2025).
20.
Peccei, R.D.; Quinn, H.R. CP Conservation in the Presence of Instantons. Phys. Rev. Lett. 1977, 38, 1440–1443.
21.
Peccei, R.D.; Quinn, H.R. Constraints Imposed by CP Conservation in the Presence of Instantons. Phys. Rev. D 1977, 16, 1791–1797.
22.
Kim, J.E. Weak Interaction Singlet and Strong CP Invariance. Phys. Rev. Lett. 1979, 43, 103.
23.
Shifman, M.A.; Vainshtein, A.I.; Zakharov, V.I. Can Confinement Ensure Natural CP Invariance of Strong Interactions? Nucl. Phys. B 1980, 166, 493–506.
24.
Dine, M.; Fischler, W.; Srednicki, M. A Simple Solution to the Strong CP Problem with a Harmless Axion. Phys. Lett. B 1981, 104, 199–202.
25.
Zhitnitsky, A.R. On Possible Suppression of the Axion Hadron Interactions. Sov. J. Nucl. Phys. 1980, 31, 260. (In Russian)
26.
Raffelt, G.G. Astrophysical methods to constrain axions and other novel particle phenomena. Phys. Rep. 1990, 198, 1–113.
27.
Miller Bertolami, M.M.; Melendez, B.E.; Althaus, L.G.; et al. Revisiting the axion bounds from the Galactic white dwarf luminosity function. J. Cosmol. Astropart. Phys. 2014, 10, 069.
28.
Ayala, A.; Dom´ınguez, I.; Giannotti, M.; et al. Revisiting the bound on axion-photon coupling from Globular Clusters. Phys. Rev. Lett. 2014, 113, 191302.
29.
Dolan, M.J.; Hiskens, F.J.; Volkas, R.R. Advancing globular cluster constraints on the axion-photon coupling. J. Cosmol. Astropart. Phys. 2022, 10, 096.
30.
Bar, N.; Blum, K.; D’Amico, G. Is there a supernova bound on axions? Phys. Rev. D 2020, 101, 123025.
31.
Chang, J.H.; Essig, R.; McDermott, S.D. Supernova 1987A Constraints on Sub-GeV Dark Sectors, Millicharged Particles, the QCD Axion, and an Axion-like Particle. J. High Energy Phys. 2018, 2018, 51.
32.
Carenza, P.; Fore, B.; Giannotti, M.; et al. Enhanced Supernova Axion Emission and its Implications. Phys. Rev. Lett. 2021, 126, 071102.
33.
Notari, A.; Rompineve, F.; Villadoro, G. Improved Hot Dark Matter Bound on the QCD Axion. Phys. Rev. Lett. 2023, 131, 011004.
34.
Gorghetto, M.; Hardy, E.; Villadoro, G. Axions from Strings: The Attractive Solution. J. High Energy Phys. 2018, 2018, 151.
35.
Gorghetto, M.; Hardy, E.; Villadoro, G. More axions from strings. SciPost Phys. 2021, 10, 050.
36.
Buschmann, M.; Foster, J.W.; Hook, A.; et al. Dark matter from axion strings with adaptive mesh refinement. Nat. Commun. 2022, 13, 1049.
37.
Saikawa, K.; Redondo, J.; Vaquero, A.; et al. Spectrum of global string networks and the axion dark matter mass. J. Cosmol. Astropart. Phys. 2024, 10, 043.
38.
Abac, A.G.; Abouelfettouh, I.; Acernese, F.; et al. Upper Limits on the Isotropic Gravitational-Wave Background from the first part of LIGO, Virgo, and KAGRA’s fourth Observing Run. arXiv 2025, arXiv:2508.20721.
39.
Abac, A.G.; Abouelfettouh, I.; Acernese, F.; et al. Cosmological and High Energy Physics implications from gravitationalwave background searches in LIGO-Virgo-KAGRA’s O1-O4a runs. arXiv 2025, arXiv:2510.26848.
40.
Available online: https://www.et-gw.eu/ (accessed on 10 November 2025).
41.
Available online: https://cosmicexplorer.org/ (accessed on 10 November 2025).
42.
Maggiore, M.; Iacovelli, F.; Belgacem, E.; et al. Comparison of global networks of third-generation gravitational-wave detectors. Class. Quant. Grav. 2025, 42, 215004.
43.
Branchesi, M.; Maggiore, M.; Alonso, D.; et al. Science with the Einstein Telescope: A comparison of different designs. J. Cosmol. Astropart. Phys. 2023, 2023, 068.
44.
Bellie, D.S.; Banagiri, S.; Doctor, Z.; et al. The unresolved stochastic background from compact binary mergers detectable by next-generation ground-based gravitational-wave observatories. Phys. Rev. D 2024, 110, 023006.
45.
Zhou, B.; Reali, L.; Berti, E.; et al. Compact Binary Foreground Subtraction in Next-Generation Ground-Based Observatories. arXiv 2022, arXiv:2209.01221.
46.
Zhou, B.; Reali, L.; Berti, E.; et al. Subtracting compact binary foregrounds to search for subdominant gravitational-wave backgrounds in next-generation ground-based observatories. Phys. Rev. D 2023, 108, 064040.
47.
Abac, A.; Abramo, R.; Albanesi, S.; et al. The Science of the Einstein Telescope. arXiv 2025, arXiv:2503.12263.
48.
Von Harling, B.; Pomarol, A.; Pujol`as, O.; et al. Peccei-Quinn Phase Transition at LIGO. J. High Energy Phys. 2020, 2020, 195.
49.
Zambujal Ferreira, R.; Notari, A.; Pujol`as, O.; et al. High Quality QCD Axion at Gravitational Wave Observatories. Phys. Rev. Lett. 2022, 128, 141101.
50.
Available online: https://www.esa.int/Science Exploration/Space Science/LISA (accessed on 10 November 2025).
51.
Binetruy, P.; Bohe, A.; Caprini, C.; et al. Cosmological Backgrounds of Gravitational Waves and eLISA/NGO: Phase Transitions, Cosmic Strings and Other Sources. J. Cosmol. Astropart. Phys. 2012, 2012, 027.
52.
Caprini, C.; Hindmarsh, M.; Huber, S.; et al. Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions. J. Cosmol. Astropart. Phys. 2016, 2016, 001.
53.
Caprini, C.; Chala, M.; Dorsch, G.C.; et al. Detecting gravitational waves from cosmological phase transitions with LISA: An update. J. Cosmol. Astropart. Phys. 2020, 2020, 024.
54.
Farmer, A.J.; Phinney, E.S. The gravitational wave background from cosmological compact binaries. Mon. Not. Roy. Astron. Soc. 2003, 346, 1197.
55.
Lamberts, A.; Blunt, S.; Littenberg, T.B.; et al. Predicting the LISA white dwarf binary population in the Milky Way with cosmological simulations. Mon. Not. Roy. Astron. Soc. 2019, 490, 5888–5903.
56.
Staelens, S.; Nelemans, G. Likelihood of white dwarf binaries to dominate the astrophysical gravitational wave background in the mHz band. Astron. Astrophys. 2024, 683, A139.
57.
Korol, V.; Hallakoun, N.; Toonen, S.; et al. Observationally driven Galactic double white dwarf population for LISA. Mon. Not. Roy. Astron. Soc. 2022, 511, 5936–5947.
58.
Karnesis, N.; Babak, S.; Pieroni, M.; et al. Characterization of the stochastic signal originating from compact binary populations as measured by LISA. Phys. Rev. D 2021, 104, 043019.
59.
Babak, S.; Caprini, C.; Figueroa, D.G.; et al. Stochastic gravitational wave background from stellar origin binary black holes in LISA. J. Cosmol. Astropart. Phys. 2023, 2023, 034.
60.
Lehoucq, L.; Dvorkin, I.; Srinivasan, R.; et al. Astrophysical uncertainties in the gravitational-wave background from stellar-mass compact binary mergers. Mon. Not. Roy. Astron. Soc. 2023, 526, 4378–4387.
61.
Piarulli, M.; Buscicchio, R.; Pozzoli, F.; et al. Test for LISA foreground Gaussianity and stationarity: Extreme mass-ratio inspirals. Phys. Rev. D 2025, 111, 103047.
62.
Antoniadis, J.; Arumugam, P.; Arumugam, S.; et al. The second data release from the European Pulsar Timing Array—III. Search for gravitational wave signals. Astron. Astrophys. 2023, 678, A50.
63.
Agazie, G.; Anumarlapudi, A.; Archibald, A.M.; et al. The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background. Astrophys. J. Lett. 2023, 951, L8.
64.
Reardon, D.J.; Zic, A.; Shannon, R.M.; et al. Search for an Isotropic Gravitational-wave Background with the Parkes Pulsar Timing Array. Astrophys. J. Lett. 2023, 951, L6.
65.
Xu, H.; Chen, S.; Guo, Y.; et al. Searching for the Nano-Hertz Stochastic Gravitational Wave Background with the Chinese Pulsar Timing Array Data Release I. Res. Astron. Astrophys. 2023, 23, 075024.
66.
Antoniadis, J.; Arzoumanian, Z.; Babak, S.; et al. The International Pulsar Timing Array second data release: Search for an isotropic gravitational wave background. Mon. Not. Roy. Astron. Soc. 2022, 510, 4873–4887.
67.
Rawlings, S.; Schilizzi, R. The Square Kilometre Array. arXiv 2011, arXiv:1105.5953.
68.
Janssen, G.; Hobbs, G.; McLaughlin, M.; et al. Gravitational wave astronomy with the SKA. Proc. Sci. 2015, AASKA14, 037.
69.
Antoniadis, J.; Arumugam, P.; Arumugam, S.; et al. The second data release from the European Pulsar Timing Array: V. Implications for massive black holes, dark matter and the early Universe. Astron. Astrophys. 2023, 685, A94.
70.
Agazie, G.; Anumarlapudi, A.; Archibald, A.M.; et al. The NANOGrav 15 yr Data Set: Constraints on Supermassive Black Hole Binaries from the Gravitational-wave Background. Astrophys. J. Lett. 2023, 952, L37.
71.
Figueroa, D.G.; Pieroni, M.; Ricciardone, A.; et al. Cosmological Background Interpretation of Pulsar Timing Array Data. Phys. Rev. Lett. 2024, 132, 171002.
72.
Ellis, J.; Fairbairn, M.; Franciolini, G.; et al. What is the source of the PTA GW signal? Phys. Rev. D 2024, 109, 023522.
73.
Afzal, A.; Agazie, G.; Anumarlapudi, A.; et al. The NANOGrav 15 yr Data Set: Search for Signals from New Physics. Astrophys. J. Lett. 2023, 951, L11.
74.
Caprini, C.; Durrer, R.; Siemens, X. Detection of gravitational waves from the QCD phase transition with pulsar timing arrays. Phys. Rev. D 2010, 82, 063511.
75.
Neronov, A.; Roper Pol, A.; Caprini, C.; et al. NANOGrav signal from magnetohydrodynamic turbulence at the QCD phase transition in the early Universe. Phys. Rev. D 2021, 103, 041302.
76.
Roper Pol, A.; Caprini, C.; Neronov, A.; et al. Gravitational wave signal from primordial magnetic fields in the Pulsar Timing Array frequency band. Phys. Rev. D 2022, 105, 123502.
77.
Cline, J.M.; Laurent, B. Bubble wall velocity for first-order QCD phase transition. Phys. Rev. D 2025, 111, 083522.
78.
Zheng, H.W.; Gao, F.; Bian, L.; et al. Quantitative analysis of the gravitational wave spectrum sourced from a first-order chiral phase transition of QCD. Phys. Rev. D 2025, 111, L021303.
79.
Sedda, M.A.; Berry, C.P.; Jani, K.; et al. The missing link in gravitational-wave astronomy: Discoveries waiting in the decihertz range. Class. Quant. Grav. 2020, 37, 215011.
80.
Perego, A.; Bonetti, M.; Sesana, A.; et al. Assessing the performance of future space-based detectors: astrophysical foregrounds and individual sources. arXiv 2025, arXiv:2510.18695.
81.
El-Neaj, Y.A.; Alpigiani, C.; Amairi-Pyka, S.; et al. AEDGE: Atomic Experiment for Dark Matter and Gravity Exploration in Space. EPJ Quant. Technol. 2020, 7, 6.
82.
Badurina, L.; Bentine, E.; Blas, D.; et al. AION: An Atom Interferometer Observatory and Network. J. Cosmol. Astropart. Phys. 2020, 2020, 011.
83.
Baynham, C.F.A.; Hobson, R.; Buchmueller, O.; et al. A Prototype Atom Interferometer to Detect Dark Matter and Gravitational Waves. arXiv 2025, arXiv:2504.09158.
84.
Abend, S.; Allard, B.; Alonso, I.; et al. Terrestrial Very-Long-Baseline Atom Interferometry: Workshop Summary. AVS Quantum Sci. 2024, 6, 02470.
85.
Abdalla, A.; Abe, M.; Abend, S.; et al. Terrestrial Very-Long-Baseline Atom Interferometry: Summary of the second workshop. EPJ Quant. Technol. 2025, 12, 42.
86.
Ajith, P.; Seoane, P.A.; Sedda, M.A.; et al. The Lunar Gravitational-wave Antenna: Mission studies and science case. arXiv 2025, arXiv:2509.25952.
87.
Jani, K.; Abernathy, M.; Berti, E.; et al. Laser Interferometer Lunar Antenna (LILA): Advancing the U.S. Priorities in Gravitational-wave and Lunar Science. arXiv 2025, arXiv:2508.11631.
88.
Book, L.G.; Flanagan, E.E. Astrometric Effects of a Stochastic Gravitational Wave Background. Phys. Rev. D 2011, 83, 024024.
89.
Mihaylov, D.P.; Moore, C.J.; et al. Astrometric Effects of Gravitational Wave Backgrounds with non-Einsteinian Polarizations. Phys. Rev. D 2018, 97, 124058.
90.
Moore, C.J.; Mihaylov, D.P.; Lasenby, A.; et al. Astrometric Search Method for Individually Resolvable Gravitational Wave Sources with Gaia. Phys. Rev. Lett. 2017, 119, 261102.
91.
Crosta, M.; Lattanzi, M.G.; Le Poncin-Lafitte, C.; et al. Pinpointing gravitational waves via astrometric gravitational wave antennas. Sci. Rep. 2024, 14, 5074.
92.
Klioner, S.A. Gaia-like astrometry and gravitational waves. Class. Quant. Grav. 2018, 35, 045005.
93.
Darling, J.; Truebenbach, A.E.; Paine, J. Astrometric Limits on the Stochastic Gravitational Wave Background. Astrophys. J. 2018, 861, 113.
94.
Garcia-Bellido, J.; Murayama, H.; White, G. Exploring the early Universe with Gaia and Theia. J. Cosmol. Astropart. Phys. 2021, 12, 023.
95.
Aggarwal, N.; Aguiar, O.D.; Bauswein, A.; et al. Challenges and opportunities of gravitational-wave searches at MHz to GHz frequencies. Living Rev. Rel. 2021, 24, 4.
96.
Aggarwal, N.; Aguiar, O.D.; Blas, D.; et al. Challenges and Opportunities of Gravitational Wave Searches above 10 kHz. arXiv 2025, arXiv:2501.11723.
97.
Domcke, V.; Ellis, S.A.R.; Kopp, J. Dielectric haloscopes as gravitational wave detectors. Phys. Rev. D 2025, 111, 035031.
98.
Berlin, A.; Blas, D.; Tito D’Agnolo, R.; et al. Electromagnetic cavities as mechanical bars for gravitational waves. Phys. Rev. D 2023, 108, 084058.
99.
Domcke, V.; Garcia-Cely, C.; Rodd, N.L. Novel Search for High-Frequency Gravitational Waves with Low-Mass Axion Haloscopes. Phys. Rev. Lett. 2022, 129, 041101.
100.
Aghanim, N.; Akrami, Y.; Ashdown, M.; et al. Planck 2018 results. VI. Cosmological parameters. Astron. Astrophys. 2020, 641, A6.
101.
Caldwell, R.; Cui, Y.; Guo, H.K.; et al. Detection of early-universe gravitational-wave signatures and fundamental physics. Gen. Rel. Grav. 2022, 54, 156.
102.
Roshan, R.; White, G. Using gravitational waves to see the first second of the Universe. Rev. Mod. Phys. 2024, 97, 015001.
103.
Vilenkin, A.; Shellard, E.P.S. Cosmic Strings and Other Topological Defects; Cambridge University Press: Cambridge, UK, 2000.
104.
Hindmarsh, M.B.; Kibble, T.W.B. Cosmic Strings. Rep. Prog. Phys. 1995, 58, 477–562.
105.
Vachaspati, T.; Pogosian, L.; Steer, D. Cosmic Strings. Scholarpedia 2015, 10, 31682.
106.
Kosowsky, A.; Turner, M.S.; Watkins, R. Gravitational radiation from colliding vacuum bubbles. Phys. Rev. D 1992, 45, 4514–4535.
107.
Kosowsky, A.; Turner, M.S. Gravitational radiation from colliding vacuum bubbles: Envelope approximation to many bubble collisions. Phys. Rev. D 1993, 47, 4372–4391.
108.
Huber, S.J.; Konstandin, T. GravitationalWave Production by Collisions: More Bubbles. J. Cosmol. Astropart. Phys. 2008, 2008, 22.
109.
Cutting, D.; Hindmarsh, M.; Weir, D.J. Gravitational waves from vacuum first-order phase transitions: From the envelope to the lattice. Phys. Rev. D 2018, 97, 123513.
110.
Cutting, D.; Escartin, E.G.; Hindmarsh, M.; et al. Gravitational waves from vacuum first order phase transitions II: from thin to thick walls. Phys. Rev. D 2021, 103, 023531.
111.
Caprini, C.; Durrer, R.; Servant, G. Gravitational wave generation from bubble collisions in first-order phase transitions: An analytic approach. Phys. Rev. D 2008, 77, 124015.
112.
Jinno, R.; Takimoto, M. Gravitational waves from bubble collisions: An analytic derivation. Phys. Rev. D 2017, 95, 024009.
113.
Kamionkowski, M.; Kosowsky, A.; Turner, M.S. Gravitational radiation from first order phase transitions. Phys. Rev. D 1994, 49, 2837–2851.
114.
Espinosa, J.R.; Konstandin, T.; No, J.M.; et al. Energy Budget of Cosmological First-order Phase Transitions. J. Cosmol. Astropart. Phys. 2010, 2010, 028.
115.
Konstandin, T. Gravitational radiation from a bulk flow model. J. Cosmol. Astropart. Phys. 2018, 2018, 047.
116.
Ellis, J.; Lewicki, M.; No, J.M.; et al. Gravitational wave energy budget in strongly supercooled phase transitions. J. Cosmol. Astropart. Phys. 2019, 1906, 024.
117.
Lewicki, M.; Vaskonen, V. Gravitational waves from bubble collisions and fluid motion in strongly supercooled phase transitions. Eur. Phys. J. C 2023, 83, 109.
118.
Hogan, C.J. Gravitational radiation from cosmological phase transitions. Mon. Not. Roy. Astron. Soc. 1986, 218, 629–636.
119.
Hindmarsh, M.; Huber, S.J.; Rummukainen, K.; et al. Numerical simulations of acoustically generated gravitational waves at a first order phase transition. Phys. Rev. D 2015, 92, 123009.
120.
Hindmarsh, M.; Huber, S.J.; Rummukainen, K.; et al. Shape of the acoustic gravitational wave power spectrum from a first order phase transition. Phys. Rev. D 2017, 96, 103520.
121.
Cutting, D.; Hindmarsh, M.; Weir, D.J. Vorticity, kinetic energy, and suppressed gravitational wave production in strong first order phase transitions. Phys. Rev. Lett. 2020, 125, 021302.
122.
Hindmarsh, M.; Hijazi, M. Gravitational waves from first order cosmological phase transitions in the Sound Shell Model. J. Cosmol. Astropart. Phys. 2019, 12, 062.
123.
Dolgov, A.D.; Grasso, D.; Nicolis, A. Relic backgrounds of gravitational waves from cosmic turbulence. Phys. Rev. D 2002, 66, 103505.
124.
Caprini, C.; Durrer, R. Gravitational waves from stochastic relativistic sources: Primordial turbulence and magnetic fields. Phys. Rev. D 2006, 74, 063521.
125.
Gogoberidze, G.; Kahniashvili, T.; Kosowsky, A. The Spectrum of Gravitational Radiation from Primordial Turbulence. Phys. Rev. D 2007, 76, 083002.
126.
Kahniashvili, T.; Campanelli, L.; Gogoberidze, G.; et al. Gravitational Radiation from Primordial Helical Inverse Cascade MHD Turbulence. Phys. Rev. D 2008, 78, 123006. Erratum in Phys. Rev. D 2009, 79, 109901.
127.
Caprini, C.; Durrer, R.; Servant, G. The stochastic gravitational wave background from turbulence and magnetic fields generated by a first-order phase transition. J. Cosmol. Astropart. Phys. 2009, 12, 024.
128.
Brandenburg, A.; Kahniashvili, T.; Mandal, S.; et al. Evolution of hydromagnetic turbulence from the electroweak phase transition. Phys. Rev. D 2017, 96, 123528.
129.
Niksa, P.; Schlederer, M.; Sigl, G. Gravitational Waves produced by Compressible MHD Turbulence from Cosmological Phase Transitions. Class. Quantum Gravity 2018, 35, 144001.
130.
Roper Pol, A.; Mandal, S.; Brandenburg, A.; et al. Numerical simulations of gravitational waves from early-universe turbulence. Phys. Rev. D 2020, 102, 083512.
131.
Auclair, P.; Caprini, C.; Cutting, D.; et al. Generation of gravitational waves from freely decaying turbulence. J. Cosmol. Astropart. Phys. 2022, 2022, 29.
132.
Caprini, C.; Durrer, R. Gravitational wave production: A Strong constraint on primordial magnetic fields. Phys. Rev. D 2001, 65, 023517.
133.
Caprini, C.; Durrer, R.; Fenu, E. Can the observed large scale magnetic fields be seeded by helical primordial fields? J. Cosmol. Astropart. Phys. 2009, 11, 001.
134.
Kahniashvili, T.; Gogoberidze, G.; Ratra, B. Gravitational Radiation from Primordial Helical MHD Turbulence. Phys. Rev. Lett. 2008, 100, 231301.
135.
Kahniashvili, T.; Kisslinger, L.; Stevens, T. Gravitational Radiation Generated by Magnetic Fields in Cosmological Phase Transitions. Phys. Rev. D 2010, 81, 023004.
136.
Durrer, R.; Neronov, A. Cosmological Magnetic Fields: Their Generation, Evolution and Observation. Astron. Astrophys. Rev. 2013, 21, 62.
137.
Baym, G.; Bodeker, D.; McLerran, L.D. Magnetic fields produced by phase transition bubbles in the electroweak phase transition. Phys. Rev. D 1996, 53, 662–667.
138.
Cheng, B.l.; Olinto, A.V. Primordial magnetic fields generated in the quark—hadron transition. Phys. Rev. D 1994, 50, 2421–2424.
139.
Sigl, G.; Olinto, A.V.; Jedamzik, K. Primordial magnetic fields from cosmological first order phase transitions. Phys. Rev. D 1997, 55, 4582–4590.
140.
Giudice, G.F.; Lee, H.M.; Pomarol, A.; et al. Nonthermal Heavy Dark Matter from a First-Order Phase Transition. arXiv 2024, arXiv:hep-ph/2403.03252.
141.
Cataldi, M.; Shakya, B. Leptogenesis via Bubble Collisions. arXiv 2024, arXiv:hep-ph/2407.16747.
142.
Jinno, R.; Shakya, B.; van de Vis, J. Gravitational Waves from Feebly Interacting Particles in a First Order Phase Transition. arXiv 2022, arXiv:gr-qc/2211.06405.
143.
Inomata, K.; Kamionkowski, M.; Kasai, K.; et al. Gravitational waves from particles produced from bubble collisions in first-order phase transitions. Phys. Rev. D 2025, 112, 083523.
144.
Durrer, R.; Kunz, M.; Melchiorri, A. Cosmic structure formation with topological defects. Phys. Rep. 2002, 364, 1–81.
145.
Figueroa, D.G.; Hindmarsh, M.; Urrestilla, J. Exact Scale-Invariant Background of Gravitational Waves from Cosmic Defects. Phys. Rev. Lett. 2013, 110, 101302.
146.
Auclair, P.; Blanco-Pillado, J.J.; Figueroa, D.G.; et al. Probing the gravitational wave background from cosmic strings with LISA. J. Cosmol. Astropart. Phys. 2020, 2020, 034.
147.
Simakachorn, P. Charting Cosmological History and New Particle Physics with Primordial Gravitational Waves. Ph.D. Thesis, Universit¨at Hamburg, Hamburg, Germany, 2022.
148.
Kibble, T.W.B. Topology of Cosmic Domains and Strings. J. Phys. A 1976, 9, 1387–1398.
149.
Durrer, R. Topological defects in cosmology. New Astron. Rev. 1999, 43, 111–156.
150.
Saikawa, K. A review of gravitational waves from cosmic domain walls. Universe 2017, 3, 40.
151.
Damour, T.; Vilenkin, A. Gravitational wave bursts from cosmic strings. Phys. Rev. Lett. 2000, 85, 3761–3764.
152.
Damour, T.; Vilenkin, A. Gravitational wave bursts from cusps and kinks on cosmic strings. Phys. Rev. D 2001, 64, 064008.
153.
Binetruy, P.; Bohe, A.; Hertog, T.; et al. Gravitational Wave Bursts from Cosmic Superstrings with Y-junctions. Phys. Rev. D 2009, 80, 123510.
154.
Kalb, M.; Ramond, P. Classical direct interstring action. Phys. Rev. D 1974, 9, 2273–2284.
155.
Davis, R.; Shellard, E. Antisymmetric tensors and spontaneous symmetry breaking. Phys. Lett. B 1988, 214, 219–222.
156.
Harari, D.; Sikivie, P. On the evolution of global strings in the early universe. Phys. Lett. B 1987, 195, 361–365.
157.
Davis, R.L. Goldstone bosons in string models of galaxy formation. Phys. Rev. D 1985, 32, 3172–3177.
158.
Battye, R.A.; Shellard, E.P.S. Recent perspectives on axion cosmology. arXiv 1997, arXiv:astro-ph/9706014.
159.
Brandenberger, R.H. On the Decay of Cosmic String Loops. Nucl. Phys. 1987, B293, 812–828.
160.
Vachaspati, T. Cosmic Rays from Cosmic Strings with Condensates. Phys. Rev. 2010, D81, 043531.
161.
Long, A.J.; Hyde, J.M.; Vachaspati, T. Cosmic Strings in Hidden Sectors: 1. Radiation of Standard Model Particles. J. Cosmol. Astropart. Phys. 2014, 1409, 030.
162.
MacGibbon, J.H.; Brandenberger, R.H. High-energy neutrino flux from ordinary cosmic strings. Nucl. Phys. B 1990, 331, 153–172.
163.
Steer, D.A.; Vachaspati, T. Light from Cosmic Strings. Phys. Rev. D 2011, 83, 043528.
164.
Vachaspati, T. Kinks and Domain Walls: An Introduction to Classical and Quantum Solitons; Cambridge University Press: Cambridge, UK, 2010.
165.
Kitajima, N.; Lee, J.; Murai, K.; et al. Gravitational Waves from Domain Wall Collapse, and Application to Nanohertz Signals with QCD-coupled Axions. arXiv 2023, arXiv:hep-ph/2306.17146.
166.
Ferreira, R.Z.; Notari, A.; Pujol`as, O.; et al. Collapsing Domain Wall Networks: Impact on Pulsar Timing Arrays and Primordial Black Holes. arXiv 2024, arXiv:astro-ph.CO/2401.14331.
167.
Ade, P.A.R.; Aghanim, N.; Armitage-Caplan, C.; et al. Planck 2013 results. XXV. Searches for cosmic strings and other topological defects. Astron. Astrophys. 2014, 571, A25.
168.
Ringeval, C. Cosmic strings and their induced non-Gaussianities in the cosmic microwave background. Adv. Astron. 2010, 2010, 380507.
169.
Aoki, Y.; Endrodi, G.; Fodor, Z.; et al. The Order of the quantum chromodynamics transition predicted by the standard model of particle physics. Nature 2006, 443, 675–678.
170.
Stephanov, M.A. QCD phase diagram: An Overview. PoS 2006, LAT2006, 024.
171.
Gurtler, M.; Ilgenfritz, E.M.; Schiller, A. Where the electroweak phase transition ends. Phys. Rev. D 1997, 56, 3888–3895.
172.
Aoki, Y. Four-dimensional simulation of the hot electroweak phase transition with the SU(2) gauge Higgs model. Phys. Rev. D 1997, 56, 3860–3865.
173.
Kajantie, K.; Laine, M.; Rummukainen, K.; et al. The Electroweak phase transition: A Nonperturbative analysis. Nucl. Phys. B 1996, 466, 189–258.
174.
Kajantie, K.; Laine, M.; Rummukainen, K.; et al. Is there a hot electroweak phase transition at mH ≳ mW? Phys. Rev. Lett. 1996, 77, 2887–2890.
175.
Laine, M.; Rummukainen, K. What’s new with the electroweak phase transition? Nucl. Phys. B Proc. Suppl. 1999, 73, 180–185.
176.
Ghiglieri, J.; Jackson, G.; Laine, M.; et al. Gravitational wave background from Standard Model physics: Complete leading order. J. High Energy Phys. 2020, 2020, 92.
177.
McDonald, J. Electroweak baryogenesis and dark matter via a gauge singlet scalar. Phys. Lett. B 1994, 323, 339–346.
178.
Espinosa, J.R.; Quiros, M. The Electroweak phase transition with a singlet. Phys. Lett. B 1993, 305, 98–105.
179.
Espinosa, J.R.; Quiros, M. Novel Effects in Electroweak Breaking from a Hidden Sector. Phys. Rev. D 2007, 76, 076004.
180.
Profumo, S.; Ramsey-Musolf, M.J.; Shaughnessy, G. Singlet Higgs phenomenology and the electroweak phase transition. J. High Energy Phys. 2007, 2007, 010.
181.
Espinosa, J.R.; Konstandin, T.; Riva, F. Strong Electroweak Phase Transitions in the Standard Model with a Singlet. Nucl. Phys. 2012, B854, 592–630.
182.
Barger, V.; Chung, D.J.H.; Long, A.J.; et al. Strongly First Order Phase Transitions Near an Enhanced Discrete Symmetry Point. Phys. Lett. B 2012, 710, 1–7.
183.
Cline, J.M.; Kainulainen, K. Electroweak baryogenesis and dark matter from a singlet Higgs. J. Cosmol. Astropart. Phys. 2013, 2013, 012.
184.
Alanne, T.; Tuominen, K.; Vaskonen, V. Strong phase transition, dark matter and vacuum stability from simple hidden sectors. Nucl. Phys. B 2014, 889, 692–711.
185.
Curtin, D.; Meade, P.; Yu, C.T. Testing Electroweak Baryogenesis with Future Colliders. J. High Energy Phys. 2014, 11, 127.
186.
Vaskonen, V. Electroweak baryogenesis and gravitational waves from a real scalar singlet. Phys. Rev. D 2017, 95, 123515.
187.
Kurup, G.; Perelstein, M. Dynamics of Electroweak Phase Transition In Singlet-Scalar Extension of the Standard Model. Phys. Rev. 2017, D96, 015036.
188.
Beniwal, A.; Lewicki, M.; Wells, J.D.; et al. Gravitational wave, collider and dark matter signals from a scalar singlet electroweak baryogenesis. J. High Energy Phys. 2017, 08, 108.
189.
Niemi, L.; Schicho, P.; Tenkanen, T.V.I. Singlet-assisted electroweak phase transition at two loops. Phys. Rev. D 2021, 103, 115035. Erratum in Phys. Rev. D 2024, 109, 039902.
190.
Lewicki, M.; Merchand, M.; Zych, M. Electroweak bubble wall expansion: gravitational waves and baryogenesis in Standard Model-like thermal plasma. J. High Energy Phys. 2022, 2022, 17.
191.
Ellis, J.; Lewicki, M.; Merchand, M.; et al. The scalar singlet extension of the Standard Model: gravitational waves versus baryogenesis. J. High Energy Phys. 2023, 2023, 93.
192.
Dev, P.S.B.; Ferrer, F.; Zhang, Y.; et al. Gravitational Waves from First-Order Phase Transition in a Simple Axion-Like Particle Model. J. Cosmol. Astropart. Phys. 2019, 1911, 006.
193.
Craig, N.; Lou, H.K.; McCullough, M.; et al. The Higgs Portal Above Threshold. J. High Energy Phys. 2016, 2016, 127.
194.
Morrissey, D.E.; Ramsey-Musolf, M.J. Electroweak baryogenesis. New J. Phys. 2012, 14, 125003.
195.
Huang, F.P.; Qian, Z.; Zhang, M. Exploring dynamical CP violation induced baryogenesis by gravitational waves and colliders. Phys. Rev. 2018, D98, 015014.
196.
Azatov, A.; Barni, G.; Chakraborty, S.; et al. Ultra-relativistic bubbles from the simplest Higgs portal and their cosmological consequences. J. High Energy Phys. 2022, 10, 017.
197.
Cline, J.M.; Friedlander, A.; He, D.M.; et al. Baryogenesis and gravity waves from a UV-completed electroweak phase transition. Phys. Rev. D 2021, 103, 123529.
198.
Huet, P.; Nelson, A.E. CP violation and electroweak baryogenesis in extensions of the standard model. Phys. Lett. 1995, B355, 229–235.
199.
Cline, J.M.; Lemieux, P.A. Electroweak phase transition in two Higgs doublet models. Phys. Rev. 1997, D55, 3873–3881.
200.
Fromme, L.; Huber, S.J.; Seniuch, M. Baryogenesis in the two-Higgs doublet model. J. High Energy Phys. 2006, 11, 038.
201.
Cline, J.M.; Kainulainen, K.; Trott, M. Electroweak Baryogenesis in Two Higgs Doublet Models and B meson anomalies. J. High Energy Phys. 2011, 11, 089.
202.
Dorsch, G.C.; Huber, S.J.; No, J.M. A strong electroweak phase transition in the 2HDM after LHC8. J. High Energy Phys. 2013, 10, 029.
203.
Dorsch, G.C.; Huber, S.J.; Mimasu, K.; et al. Echoes of the Electroweak Phase Transition: Discovering a second Higgs doublet through A0 → ZH0. Phys. Rev. Lett. 2014, 113, 211802.
204.
Kakizaki, M.; Kanemura, S.; Matsui, T. Gravitational waves as a probe of extended scalar sectors with the first order electroweak phase transition. Phys. Rev. 2015, D92, 115007.
205.
Dorsch, G.C.; Huber, S.J.; Konstandin, T.; et al. A Second Higgs Doublet in the Early Universe: Baryogenesis and Gravitational Waves. J. Cosmol. Astropart. Phys. 2017, 1705, 052.
206.
Basler, P.; Krause, M.; Muhlleitner, M.; et al. Strong First Order Electroweak Phase Transition in the CP-Conserving 2HDM Revisited. J. High Energy Phys. 2017, 2017, 121.
207.
Dorsch, G.C.; Huber, S.J.; Mimasu, K.; et al. The Higgs Vacuum Uplifted: Revisiting the Electroweak Phase Transition with a Second Higgs Doublet. J. High Energy Phys. 2017, 12, 086.
208.
Basler, P.; Muhlleitner, M.; Wittbrodt, J. The CP-Violating 2HDM in Light of a Strong First Order Electroweak Phase Transition and Implications for Higgs Pair Production. J. High Energy Phys. 2018, 2018, 61.
209.
Bernon, J.; Bian, L.; Jiang, Y. A new insight into the phase transition in the early Universe with two Higgs doublets. J. High Energy Phys. 2018, 2018, 151.
210.
Huang, F.P.; Yu, J.H. Exploring inert dark matter blind spots with gravitational wave signatures. Phys. Rev. 2018, D98, 095022.
211.
Patel, H.H.; Ramsey-Musolf, M.J. Stepping Into Electroweak Symmetry Breaking: Phase Transitions and Higgs Phenomenology. Phys. Rev. 2013, D88, 035013.
212.
Chala, M.; Ramos, M.; Spannowsky, M. Gravitational wave and collider probes of a triplet Higgs sector with a low cutoff. Eur. Phys. J. 2019, C79, 156.
213.
Blinov, N.; Kozaczuk, J.; Morrissey, D.E.; et al. Electroweak Baryogenesis from Exotic Electroweak Symmetry Breaking. Phys. Rev. 2015, D92, 035012.
214.
Inoue, S.; Ovanesyan, G.; Ramsey-Musolf, M.J. Two-Step Electroweak Baryogenesis. Phys. Rev. 2016, D93, 015013.
215.
Blinov, N.; Kozaczuk, J.; Morrissey, D.E.; et al. Compressing the Inert Doublet Model. Phys. Rev. 2016, D93, 035020.
216.
Huber, S.J.; Konstandin, T.; Nardini, G.; et al. Detectable Gravitational Waves from Very Strong Phase Transitions in the General NMSSM. J. Cosmol. Astropart. Phys. 2016, 1603, 036.
217.
Bian, L.; Guo, H.K.; Shu, J. Gravitational Waves, baryon asymmetry of the universe and electric dipole moment in the CP-violating NMSSM. Chin. Phys. 2018, C42, 093106.
218.
Demidov, S.V.; Gorbunov, D.S.; Kirpichnikov, D.V. Gravitational waves from phase transition in split NMSSM. Phys. Lett. 2018, B779, 191–194.
219.
Georgi, H.; Machacek, M. Doubly Charged Higgs Bosons. Nucl. Phys. 1985, B262, 463–477.
220.
Cort, L.; Garcia, M.; Quiros, M. Supersymmetric Custodial Triplets. Phys. Rev. 2013, D88, 075010.
221.
Garcia-Pepin, M.; Quiros, M. Strong electroweak phase transition from Supersymmetric Custodial Triplets. J. High Energy Phys. 2016, 2016, 177.
222.
Zhang, X.M. Operators analysis for Higgs potential and cosmological bound on Higgs mass. Phys. Rev. 1993, D47, 3065–3067.
223.
Grojean, C.; Servant, G.; Wells, J.D. First-order electroweak phase transition in the standard model with a low cutoff. Phys. Rev. 2005, D71, 036001.
224.
Delaunay, C.; Grojean, C.; Wells, J.D. Dynamics of Non-renormalizable Electroweak Symmetry Breaking. J. High Energy Phys. 2008, 2008, 29.
225.
Bodeker, D.; Fromme, L.; Huber, S.J.; et al. The Baryon asymmetry in the standard model with a low cut-off. J. High Energy Phys. 2005, 2005, 26.
226.
Harman, C.P.D.; Huber, S.J. Does zero temperature decide on the nature of the electroweak phase transition? J. High Energy Phys. 2016, 2016, 5.
227.
Damgaard, P.H.; Haarr, A.; O’Connell, D.; et al. Effective Field Theory and Electroweak Baryogenesis in the Singlet-Extended Standard Model. J. High Energy Phys. 2016, 2016, 107.
228.
de Vries, J.; Postma, M.; van de Vis, J.; et al. Electroweak Baryogenesis and the Standard Model Effective Field Theory. J. High Energy Phys. 2018, 2018, 89.
229.
Chala, M.; Krause, C.; Nardini, G. Signals of the electroweak phase transition at colliders and gravitational wave observatories. J. High Energy Phys. 2018, 2018, 62.
230.
Huber, S.J.; Konstandin, T. Production of gravitational waves in the nMSSM. J. Cosmol. Astropart. Phys. 2008, 2008, 17.
231.
Huang, F.P.; Wan, Y.; Wang, D.G.; et al. Hearing the echoes of electroweak baryogenesis with gravitational wave detectors. Phys. Rev. 2016, D94, 041702.
232.
Iso, S.; Okada, N.; Orikasa, Y. Classically conformal B⁻ L extended Standard Model. Phys. Lett. B 2009, 676, 81–87.
233.
Iso, S.; Okada, N.; Orikasa, Y. The minimal B-L model naturally realized at TeV scale. Phys. Rev. D 2009, 80, 115007.
234.
Escudero, M.; Witte, S.J.; Rius, N. The dispirited case of gauged U(1)B−L dark matter. J. High Energy Phys. 2018, 2018, 190.
235.
Dasgupta, A.; Dev, P.S.B.; Ghoshal, A.; et al. Gravitational wave pathway to testable leptogenesis. Phys. Rev. D 2022, 106, 075027.
236.
Jinno, R.; Takimoto, M. Probing a classically conformal B-L model with gravitational waves. Phys. Rev. D 2017, 95, 015020.
237.
Marzo, C.; Marzola, L.; Vaskonen, V. Phase transition and vacuum stability in the classically conformal B–L model. Eur. Phys. J. C 2019, 79, 601.
238.
Sagunski, L.; Schicho, P.; Schmitt, D. Supercool exit: Gravitational waves from QCD-triggered conformal symmetry breaking. Phys. Rev. D 2023, 107, 123512.
239.
Creminelli, P.; Nicolis, A.; Rattazzi, R. Holography and the electroweak phase transition. J. High Energy Phys. 2002, 2002, 51.
240.
Randall, L.; Servant, G. Gravitational waves from warped spacetime. J. High Energy Phys. 2007, 2007, 54.
241.
Nardini, G.; Quiros, M.; Wulzer, A. A Confining Strong First-Order Electroweak Phase Transition. J. High Energy Phys. 2007, 2007, 077.
242.
Hassanain, B.; March-Russell, J.; Schvellinger, M. Warped Deformed Throats have Faster (Electroweak) Phase Transitions. J. High Energy Phys. 2007, 10, 089.
243.
Konstandin, T.; Nardini, G.; Quiros, M. Gravitational Backreaction Effects on the Holographic Phase Transition. Phys. Rev. D 2010, 82, 083513.
244.
Konstandin, T.; Servant, G. Cosmological Consequences of Nearly Conformal Dynamics at the TeV scale. J. Cosmol. Astropart. Phys. 2011, 12, 009.
245.
Bunk, D.; Hubisz, J.; Jain, B. A Perturbative RS I Cosmological Phase Transition. Eur. Phys. J. C 2018, 78, 78.
246.
Dillon, B.M.; El-Menoufi, B.K.; Huber, S.J.; et al. Rapid holographic phase transition with brane-localized curvature. Phys. Rev. D 2018, 98, 086005.
247.
von Harling, B.; Servant, G. QCD-induced Electroweak Phase Transition. J. High Energy Phys. 2018, 2018, 159.
248.
Megıas, E.; Nardini, G.; Quiros, M. Cosmological Phase Transitions in Warped Space: Gravitational Waves and Collider Signatures. J. High Energy Phys. 2018, 2018, 95.
249.
Fujikura, K.; Nakai, Y.; Yamada, M. A more attractive scheme for radion stabilization and supercooled phase transition 2020, 2020, 111.
250.
Panico, G.; Wulzer, A. The Composite Nambu-Goldstone Higgs; Springer: Cham, Switzerland, 2016; Volume 913.
251.
Grojean, C.; Matsedonskyi, O.; Panico, G. Light top partners and precision physics. J. High Energy Phys. 2013, 2013, 160.
252.
Csaki, C.; Geller, M.; Telem, O. Tree-level Quartic for a Holographic Composite Higgs. J. High Energy Phys. 2018, 2018, 134.
253.
Grinstein, B.; Trott, M. Electroweak Baryogenesis with a Pseudo-Goldstone Higgs. Phys. Rev. D 2008, 78, 075022.
254.
Schwaller, P. Gravitational Waves from a Dark Phase Transition. Phys. Rev. Lett. 2015, 115, 181101.
255.
Jaeckel, J.; Khoze, V.V.; Spannowsky, M. Hearing the signal of dark sectors with gravitational wave detectors. arXiv 2016, arXiv:1602.03901.
256.
Chala, M.; Nardini, G.; Sobolev, I. Unified explanation for dark matter and electroweak baryogenesis with direct detection and gravitational wave signatures. arXiv 2016, arXiv:1605.08663.
257.
Addazi, A. Limiting First Order Phase Transitions in Dark Gauge Sectors from Gravitational Waves experiments. Mod. Phys. Lett. A 2017, 32, 1750049.
258.
Baldes, I. Gravitational waves from the asymmetric-dark-matter generating phase transition. J. Cosmol. Astropart. Phys. 2017, 2017, 028.
259.
Addazi, A.; Marciano, A. Gravitational waves from dark first order phase transitions and dark photons. Chin. Phys. C 2018, 42, 023107.
260.
Tsumura, K.; Yamada, M.; Yamaguchi, Y. Gravitational wave from dark sector with dark pion. J. Cosmol. Astropart. Phys. 2017, 2017, 044.
261.
Aoki, M.; Goto, H.; Kubo, J. Gravitational Waves from Hidden QCD Phase Transition. Phys. Rev. D 2017, 96, 075045.
262.
Croon, D.; White, G. Exotic Gravitational Wave Signatures from Simultaneous Phase Transitions. J. High Energy Phys. 2018, 2018, 210.
263.
Croon, D.; Sanz, V.; White, G. Model Discrimination in Gravitational Wave spectra from Dark Phase Transitions. J. High Energy Phys. 2018, 2018, 203.
264.
Baldes, I.; Garcia-Cely, C. Strong gravitational radiation from a simple dark matter model. J. High Energy Phys. 2019, 2019, 190.
265.
Madge, E.; Schwaller, P. Leptophilic dark matter from gauged lepton number: Phenomenology and gravitational wave signatures. J. High Energy Phys. 2019, 2019, 48.
266.
Breitbach, M.; Kopp, J.; Madge, E.; et al. Dark, Cold, and Noisy: Constraining Secluded Hidden Sectors with Gravitational Waves. J. Cosmol. Astropart. Phys. 2019, 2019, 007.
267.
Fairbairn, M.; Hardy, E.; Wickens, A. Hearing without seeing: gravitational waves from hot and cold hidden sectors. J. High Energy Phys. 2019, 2019, 44.
268.
Baker, M.J.; Kopp, J. Dark Matter Decay between Phase Transitions at the Weak Scale. Phys. Rev. Lett. 2017, 119, 061801.
269.
Baker, M.J.; Breitbach, M.; Kopp, J.; et al. Dynamic Freeze-In: Impact of Thermal Masses and Cosmological Phase Transitions on Dark Matter Production. J. High Energy Phys. 2017, 119, 061801.
270.
Greljo, A.; Opferkuch, T.; Stefanek, B.A. Gravitational Imprints of Flavor Hierarchies Phys. Rev. Lett. 2019, 124, 171802.
271.
Delle Rose, L.; Panico, G.; Redi, M.; et al. Gravitational Waves from Supercool Axions. J. High Energy Phys. 2020, 2020, 25.
272.
Baratella, P.; Pomarol, A.; Rompineve, F. The Supercooled Universe. J. High Energy Phys. 2019, 2019, 100.
273.
Ferreira, R.Z.; Notari, A.; Pujolas, O.; et al. Gravitational waves from domain walls in Pulsar Timing Array datasets. J. Cosmol. Astropart. Phys. 2023, 2023, 001.
274.
Holdom, B.; Peskin, M.E. Raising the Axion Mass. Nucl. Phys. B 1982, 208, 397–412.
275.
Treiman, S.B.; Wilczek, F. Axion Emission in Decay of Excited Nuclear States. Phys. Lett. B 1978, 74, 381–383.
276.
Dimopoulos, S. A Solution of the Strong CP Problem in Models With Scalars. Phys. Lett. B 1979, 84, 435–439.
277.
Tye, S.H.H. A Superstrong Force With a Heavy Axion. Phys. Rev. Lett. 1981, 47, 1035.
278.
Holdom, B. Strong QCD at High-energies and a Heavy Axion. Phys. Lett. B 1985, 154, 316.
279.
Flynn, J.M.; Randall, L. A Computation of the Small Instanton Contribution to the Axion Potential. Nucl. Phys. B 1987, 293, 731–739.
280.
Choi, K.; Do Kim, H. Small instanton contribution to the axion potential in supersymmetric models. Phys. Rev. D 1999, 59, 072001.
281.
Agrawal, P.; Howe, K. Factoring the Strong CP Problem. arXiv 2017, arXiv:1710.04213.
282.
Kitano, R.; Yin, W. Strong CP problem and axion dark matter with small instantons. J. High Energy Phys. 2021, 2021, 78.
283.
Rubakov, V.A. Grand unification and heavy axion. J. Exp. Theor. Phys. Lett. 1997, 65, 621–624.
284.
Gherghetta, T.; Nagata, N.; Shifman, M. A Visible QCD Axion from an Enlarged Color Group. Phys. Rev. D 2016, 93, 115010.
285.
Gherghetta, T.; Nguyen, M.D. A Composite Higgs with a Heavy Composite Axion. J. High Energy Phys. 2020, 2020, 94.
286.
Berezhiani, Z.; Gianfagna, L.; Giannotti, M. Strong CP problem and mirror world: The Weinberg-Wilczek axion revisited. Phys. Lett. B 2001, 500, 286–296.
287.
Dimopoulos, S.; Hook, A.; Huang, J.; et al. A collider observable QCD axion. J. High Energy Phys. 2016, 2016, 52.
288.
Hook, A.; Kumar, S.; Liu, Z.; et al. High Quality QCD Axion and the LHC. Phys. Rev. Lett. 2020, 124, 221801.
289.
Sikivie, P. Axions, Domain Walls and the Early Universe. Phys. Rev. Lett. 1982, 48, 1156–1159.
290.
Schwarz, D.J.; Stuke, M. Lepton asymmetry and the cosmic QCD transition. arXiv 2009, arXiv:0906.3434
291.
Wygas, M.M.; Oldengott, I.M.; B¨odeker, D.; et al. Cosmic QCD Epoch at Nonvanishing Lepton Asymmetry. Phys. Rev. Lett. 2018, 121, 201302.
292.
Middeldorf-Wygas, M.M.; Oldengott, I.M.; Bodeker, D.; et al. Cosmic QCD transition for large lepton flavor asymmetries. Phys. Rev. D 2022, 105, 123533.
293.
Chatterjee, A.; Frasca, M.; Ghoshal, A.; et al. Finite temperature QCD crossover at non-zero chemical potential: A Dyson–Schwinger approach. Nucl. Phys. B 2025, 1017, 116972.
294.
Ekstedt, A.; Schicho, P.; Tenkanen, T.V.I. DRalgo: A package for effective field theory approach for thermal phase transitions. Comput. Phys. Commun. 2023, 288, 108725.
295.
Ekstedt, A.; Schicho, P.; Tenkanen, T.V.I. Cosmological phase transitions at three loops: the final verdict on perturbation theory 2024. Phys. Rev. D 2024, 110, 096006.
296.
Kainulainen, K.; Keus, V.; Niemi, L.; et al. On the validity of perturbative studies of the electroweak phase transition in the Two Higgs Doublet model. J. High Energy Phys. 2019, 2019, 75.
297.
Gould, O.; Kozaczuk, J.; Niemi, L.; et al. Nonperturbative analysis of the gravitational waves from a first-order electroweak phase transition. Phys. Rev. D 2019, 100, 115024.
298.
Niemi, L.; Patel, H.H.; Ramsey-Musolf, M.J.; et al. Electroweak phase transition in the real triplet extension of the SM: Dimensional reduction. Phys. Rev. D 2019, 100, 035002.
299.
Croon, D.; Gould, O.; Schicho, P.; et al. Theoretical uncertainties for cosmological first-order phase transitions. J. High Energy Phys. 2021, 2021, 55.
300.
Kierkla, M.; Swiezewska, B.; Tenkanen, T.V.I.; et al. Gravitational waves from supercooled phase transitions: dimensional transmutation meets dimensional reduction. J. High Energy Phys. 2024, 2024, 234.
301.
Schicho, P.M.; Tenkanen, T.V.I.; Osterman, J. Robust approach to thermal resummation: Standard Model meets a singlet. J. High Energy Phys. 2021, 2021, 130.
302.
Gould, O.; Tenkanen, T.V.I. Perturbative effective field theory expansions for cosmological phase transitions. J. High Energy Phys. 2024, 2024, 48.
303.
Lewicki, M.; Merchand, M.; Sagunski, L.; et al. Impact of theoretical uncertainties on model parameter reconstruction from GW signals sourced by cosmological phase transitions Phys. Rev. D 2024, 110, 023538.
304.
Banerjee, U.; Chakraborty, S.; Prakash, S.; et al. The feasibility of ultra-relativistic bubbles in SMEFT 2024. Phys. Rev. D 2024, 110, 055002.
305.
Coleman, S.R. The Fate of the False Vacuum. 1. Semiclassical Theory. Phys. Rev. D 1977, 15, 2929–2936.
306.
Callan, C.G.; Coleman, S.R. The Fate of the False Vacuum. 2. First Quantum Corrections. Phys. Rev. D 1977, 16, 1762–1768.
307.
Linde, A.D. Fate of the False Vacuum at Finite Temperature: Theory and Applications. Phys. Lett. B 1981, 100, 37–40.
308.
Linde, A.D. Decay of the False Vacuum at Finite Temperature. Nucl. Phys. B 1983, 216, 421–445.
309.
Turner, M.S.; Weinberg, E.J.; Widrow, L.M. Bubble nucleation in first order inflation and other cosmological phase transitions. Phys. Rev. D 1992, 46, 2384–2403.
310.
Megevand, A.; Ramirez, S. Bubble nucleation and growth in very strong cosmological phase transitions. Nucl. Phys. B 2017, 919, 74–109,
311.
Hindmarsh, M.B.; Luben, M.; Lumma, J.; et al. Phase transitions in the early universe. arXiv 2021, arXiv:2008.09136.
312.
Ignatius, J.; Kajantie, K.; Kurki-Suonio, H.; et al. The growth of bubbles in cosmological phase transitions. Phys. Rev. D 1994, 49, 3854–3868.
313.
Kurki-Suonio, H.; Laine, M. On bubble growth and droplet decay in cosmological phase transitions. Phys. Rev. D 1996, 54, 7163–7171.
314.
Kurki-Suonio, H.; Laine, M. Supersonic deflagrations in cosmological phase transitions. Phys. Rev. D 1995, 51, 5431–5437.
315.
Giese, F.; Konstandin, T.; van de Vis, J. Model-independent energy budget of cosmological first-order phase transitions—A sound argument to go beyond the bag model. J. Cosmol. Astropart. Phys. 2020, 2020, 057.
316.
Available online: https://github.com/cosmoGW/cosmoGW (accessed on 10 November 2025).
317.
Ekstedt, A.; Gould, O.; Hirvonen, J.; et al. How fast does the WallGo? A package for computing wall velocities in first-order phase transitions. J. High Energy Phys. 2025, 2025, 101.
318.
Moore, G.D.; Prokopec, T. How fast can the wall move? A Study of the electroweak phase transition dynamics. Phys. Rev. D 1995, 52, 7182–7204.
319.
Moore, G.D.; Prokopec, T. Bubble wall velocity in a first order electroweak phase transition. Phys. Rev. Lett. 1995, 75, 777–780.
320.
Bodeker, D.; Moore, G.D. Can electroweak bubble walls run away? arXiv 2009, arXiv:0903.4099.
321.
Konstandin, T.; Nardini, G.; Rues, I. From Boltzmann equations to steady wall velocities. arXiv 2014, arXiv:1407.3132.
322.
Kozaczuk, J. Bubble Expansion and the Viability of Singlet-Driven Electroweak Baryogenesis. J. High Energy Phys. 2015, 2015, 135.
323.
Hoche, S.; Kozaczuk, J.; Long, A.J.; et al. Towards an all-orders calculation of the electroweak bubble wall velocity. arXiv 2021, arXiv:2007.10343.
324.
Barroso Mancha, M.; Prokopec, T.; Swiezewska, B. Field-theoretic derivation of bubble-wall force. arXiv 2021, arXiv:2005.10875.
325.
Laurent, B.; Cline, J.M. First principles determination of bubble wall velocity. Phys. Rev. D 2022, 106, 023501.
326.
Huber, S.J.; Sopena, M. An efficient approach to electroweak bubble velocities. arXiv 2013, arXiv:1302.1044.
327.
Friedlander, A.; Banta, I.; Cline, J.M.; et al. Wall speed and shape in singlet-assisted strong electroweak phase transitions. Phys. Rev. D 2021, 103, 055020.
328.
Laurent, B.; Cline, J.M. Fluid equations for fast-moving electroweak bubble walls. Phys. Rev. D 2020, 102, 063516.
329.
Dorsch, G.C.; Huber, S.J.; Konstandin, T. Bubble wall velocities in the Standard Model and beyond. arXiv 2018, arXiv:1809.04907.
330.
Jinno, R.; Takimoto, M. Gravitational waves from bubble dynamics: Beyond the Envelope. arXiv 2019, arXiv:1707.03111.
331.
Ellis, J.; Lewicki, M.; Vaskonen, V. Updated predictions for gravitational waves produced in a strongly supercooled phase transition. arXiv 2020, arXiv:2007.15586.
332.
Athron, P.; Balazs, C.; Morris, L. Supercool subtleties of cosmological phase transitions. arXiv 2023, arXiv:2212.07559.
333.
Ellis, J.; Lewicki, M.; No, J.M. On the Maximal Strength of a First-Order Electroweak Phase Transition and its Gravitational Wave Signal. arXiv 2019, arXiv:1809.08242.
334.
Child, H.L.; Giblin, J.T., Jr. Gravitational Radiation from First-Order Phase Transitions. J. Cosmol. Astropart. Phys. 2012, 2012, 001.
335.
Jinno, R.; Konstandin, T.; Takimoto, M. Relativistic bubble collisions—A closer look. J. Cosmol. Astropart. Phys. 2019, 2019, 035.
336.
Hindmarsh, M. Sound shell model for acoustic gravitational wave production at a first-order phase transition in the early Universe. Phys. Rev. Lett. 2018, 120, 071301.
337.
Cai, R.G.; Wang, S.J.; Yuwen, Z.Y. Hydrodynamic sound shell model. Phys. Rev. D 2023, 108, L021502.
338.
Roper Pol, A.; Procacci, S.; Caprini, C. Characterization of the gravitational wave spectrum from sound waves within the sound shell model. Phys. Rev. D 2024, 109, 063531.
339.
Kosowsky, A.; Mack, A.; Kahniashvili, T. Gravitational radiation from cosmological turbulence. Phys. Rev. D 2002, 66, 024030.
340.
Giombi, L.; Dahl, J.; Hindmarsh, M. Acoustic gravitational waves beyond leading order in bubble over Hubble radius. arXiv 2025, arXiv:2504.08037.
341.
Hindmarsh, M.; Huber, S.J.; Rummukainen, K.; et al. Gravitational waves from the sound of a first order phase transition. Phys. Rev. Lett. 2014, 112, 041301.
342.
Jinno, R.; Konstandin, T.; Rubira, H. A hybrid simulation of gravitational wave production in first-order phase transitions. J. Cosmol. Astropart. Phys. 2021, 2021, 014.
343.
Jinno, R.; Konstandin, T.; Rubira, H.; et al. Higgsless simulations of cosmological phase transitions and gravitational waves. J. Cosmol. Astropart. Phys. 2023, 2023, 011.
344.
Caprini, C.; Jinno, R.; Konstandin, T.; et al. Gravitational waves from decaying sources in strong phase transitions. arXiv 2024, arXiv:2409.03651.
345.
Roper Pol, A.; Brandenburg, A.; Kahniashvili, T.; et al. The timestep constraint in solving the gravitational wave equations sourced by hydromagnetic turbulence. Geophys. Astrophys. Fluid Dyn. 2020, 114, 130–161.
346.
Roper Pol, A.; Mandal, S.; Brandenburg, A.; et al. Polarization of gravitational waves from helical MHD turbulent sources. J. Cosmol. Astropart. Phys. 2022, 2022, 019.
347.
Brandenburg, A.; Gogoberidze, G.; Kahniashvili, T.; et al. The scalar, vector, and tensor modes in gravitational wave turbulence simulations. Class. Quantum Gravity 2021, 38, 145002.
348.
Correia, J.; Hindmarsh, M.; Rummukainen, K.; et al. Gravitational waves from strong first order phase transitions. arXiv 2025, arXiv:2505.17824.
349.
Sharma, R.; Dahl, J.; Brandenburg, A.; et al. Shallow relic gravitational wave spectrum with acoustic peak. J. Cosmol. Astropart. Phys. 2023, 2023, 042.
350.
Dahl, J.; Hindmarsh, M.; Rummukainen, K.; et al. Decay of acoustic turbulence in two dimensions and implications for cosmological gravitational waves. Phys. Rev. D 2022, 106, 063511.
351.
Brandenburg, A.; Johansen, A.; Bourdin, P.A.; et al. The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained. J. Open Source Softw. 2021, 6, 2807.
352.
Badger, C.; Fornal, B.; Martinovic, K.; et al. Probing early Universe supercooled phase transitions with gravitational wave data. Phys. Rev. D 2023, 107, 023511.
353.
Caprini, C.; Figueroa, D.G.; Flauger, R.; et al. Reconstructing the spectral shape of a stochastic gravitational wave background with LISA J. Cosmol. Astropart. Phys. 2019, 2019, 017.
354.
Flauger, R.; Karnesis, N.; Nardini, G.; et al. Improved reconstruction of a stochastic gravitational wave background with LISA. J. Cosmol. Astropart. Phys. 2021, 01, 059.
355.
Torrado, J.; Lewis, A. Cobaya: Code for Bayesian Analysis of hierarchical physical models. J. Cosmol. Astropart. Phys. 2021, 05, 057.
356.
Handley, W.J.; Hobson, M.P.; Lasenby, A.N. polychord: next-generation nested sampling. Mon. Not. Roy. Astron. Soc. 2015, 453, 4385–4399.
357.
Handley, W.J.; Hobson, M.P.; Lasenby, A.N. PolyChord: nested sampling for cosmology. Mon. Not. Roy. Astron. Soc. 2015, 450, L61–L65.
358.
Lewis, A. GetDist: a Python package for analysing Monte Carlo samples. J. Cosmol. Astropart. Phys. 2025, 2025, 025.
359.
Gowling, C.; Hindmarsh, M. Observational prospects for phase transitions at LISA: Fisher matrix analysis. J. Cosmol. Astropart. Phys. 2021, 2021, 039.
360.
Gowling, C.; Hindmarsh, M.; Hooper, D.C.; et al. Reconstructing physical parameters from template gravitational wave spectra at LISA: first order phase transitions. J. Cosmol. Astropart. Phys. 2023, 2023, 061.
361.
Giese, F.; Konstandin, T.; van de Vis, J. Finding sound shells in LISA mock data using likelihood sampling. J. Cosmol. Astropart. Phys. 2021, 2021, 002.
362.
Blasi, S.; Mariotti, A. Domain Walls Seeding the Electroweak Phase Transition. Phys. Rev. Lett. 2022, 129, 261303.

Scilight Press

Author Information

Abstract

Keywords

References

About Scilight

Journals

Publishing Policies

Contact Us