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About electroweak domain walls in Majoron models

Maximilian Berbig*

  • *Contact author: berbig@ific.uv.es
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Phys. Rev. D 113, 043515 – Published 13 February, 2026Erratum Phys. Rev. D 113, 109902 (2026)

DOI: https://doi.org/10.1103/5j71-nz8l

Abstract

Some time ago it was claimed in “Spontaneous breaking of lepton number and cosmological domain wall problem” [Lazarides et al. Phys. Rev. Lett. 122, 151301 (2019)] that nonperturbative instantons of the weak interaction SU(2)W lead to the formation of domain walls in Majoron models owing to the anomaly of the spontaneously broken global lepton number L symmetry U(1)L with respect to SU(2)W. We point out that it has long been known that this effect can be completely rotated away unless there is a source of explicit B+L breaking present, where B denotes the baryon number. We further estimate the tiny instanton-induced Majoron mass from B+L breaking and analyze the cosmological impact of such domain walls. In general, this scenario does not lead to a cosmological catastrophe, and we demonstrate that the tiny instanton-induced mass can act as a bias term to collapse walls induced by a larger source of lepton number breaking. Alternatively, this electroweak Majoron could act as dynamical dark energy.

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Erratum: About electroweak domain walls in Majoron models [Phys. Rev. D 113, 043515 (2026)]

Maximilian Berbig
Phys. Rev. D 113, 109902 (2026)

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References (184)

  1. Y. B. Zeldovich, I. Y. Kobzarev, and L. B. Okun, Cosmological consequences of the spontaneous breakdown of discrete symmetry, Zh. Eksp. Teor. Fiz. 67, 3 (1974).
  2. A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University Press, Cambridge, England, 2000).
  3. W. H. Press, B. S. Ryden, and D. N. Spergel, Dynamical evolution of domain walls in an expanding universe, Astrophys. J. 347, 590 (1989).
  4. T. Garagounis and M. Hindmarsh, Scaling in numerical simulations of domain walls, Phys. Rev. D 68, 103506 (2003).
  5. A. M. M. Leite, C. J. A. P. Martins, and E. P. S. Shellard, Accurate calibration of the velocity-dependent one-scale model for domain walls, Phys. Lett. B 718, 740 (2013).
  6. T. Hiramatsu, M. Kawasaki, and K. Saikawa, On the estimation of gravitational wave spectrum from cosmic domain walls, J. Cosmol. Astropart. Phys. 02 (2014) 031.
  7. G. B. Gelmini, M. Gleiser, and E. W. Kolb, Cosmology of biased discrete symmetry breaking, Phys. Rev. D 39, 1558 (1989).
  8. Y. Akrami et al. (Planck Collaboration), Planck 2018 results. X. Constraints on inflation, Astron. Astrophys. 641, A10 (2020).
  9. A. H. Guth, The inflationary universe: A possible solution to the horizon and flatness problems, Phys. Rev. D 23, 347 (1981).
  10. D. Gonzalez, N. Kitajima, F. Takahashi, and W. Yin, Stability of domain wall network with initial inflationary fluctuations and its implications for cosmic birefringence, Phys. Lett. B 843, 137990 (2023).
  11. S. Weinberg, Gauge and global symmetries at high temperature, Phys. Rev. D 9, 3357 (1974).
  12. A. Vilenkin, Gravitational field of vacuum domain walls and strings, Phys. Rev. D 23, 852 (1981).
  13. S. Ramazanov, E. Babichev, D. Gorbunov, and A. Vikman, Beyond freeze-in: Dark matter via inverse phase transition and gravitational wave signal, Phys. Rev. D 105, 063530 (2022).
  14. E. Babichev, D. Gorbunov, S. Ramazanov, and A. Vikman, Gravitational shine of dark domain walls, J. Cosmol. Astropart. Phys. 04 (2022) 028.
  15. T. W. B. Kibble, Topology of cosmic domains and strings, J. Phys. A 9, 1387 (1976).
  16. P. Sikivie, Of axions, domain walls and the early universe, Phys. Rev. Lett. 48, 1156 (1982).
  17. R. Z. Ferreira, A. Notari, O. Pujolas, and F. Rompineve, Gravitational waves from domain walls in Pulsar Timing Array datasets, J. Cosmol. Astropart. Phys. 02 (2023) 001.
  18. G. Agazie et al. (NANOGrav Collaboration), The NANOGrav 15 yr data set: Evidence for a gravitational-wave background, Astrophys. J. Lett. 951, L8 (2023).
  19. J. Antoniadis et al. (EPTA and InPTA Collaborations), The second data release from the European Pulsar Timing Array—III. Search for gravitational wave signals, Astron. Astrophys. 678, A50 (2023).
  20. D. J. Reardon et al., Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array, Astrophys. J. Lett. 951, L6 (2023).
  21. H. Xu et al., Searching for the nano-hertz stochastic gravitational wave background with the Chinese Pulsar Timing Array Data Release I, Res. Astron. Astrophys. 23, 075024 (2023).
  22. G. Agazie et al. (International Pulsar Timing Array Collaboration), Comparing recent pulsar timing array results on the nanohertz stochastic gravitational-wave background, Astrophys. J. 966, 105 (2024).
  23. S. Weinberg, A new light boson?, Phys. Rev. Lett. 40, 223 (1978).
  24. F. Wilczek, Problem of strong p and t invariance in the presence of instantons, Phys. Rev. Lett. 40, 279 (1978).
  25. R. D. Peccei and H. R. Quinn, CP conservation in the presence of pseudoparticles, Phys. Rev. Lett. 38, 1440 (1977).
  26. R. D. Peccei and H. R. Quinn, Constraints imposed by CP conservation in the presence of instantons, Phys. Rev. D 16, 1791 (1977).
  27. T. W. B. Kibble, Topology of cosmic domains and strings, J. Phys. A 9, 1387 (1976).
  28. T. W. B. Kibble, G. Lazarides, and Q. Shafi, Walls bounded by strings, Phys. Rev. D 26, 435 (1982).
  29. T. Kibble, Some implications of a cosmological phase transition, Phys. Rep. 67, 183 (1980).
  30. A. Vilenkin and A. E. Everett, Cosmic strings and domain walls in models with Goldstone and PseudoGoldstone bosons, Phys. Rev. Lett. 48, 1867 (1982).
  31. S. M. Barr, K. Choi, and J. E. Kim, Some aspects of axion cosmology in unified and superstring models, Nucl. Phys. B283, 591 (1987).
  32. K. A. Beyer and S. Sarkar, Ruling out light axions: The writing is on the wall, SciPost Phys. 15, 003 (2023).
  33. S. M. Barr and J. E. Kim, New confining force solution of the QCD axion domain-wall problem, Phys. Rev. Lett. 113, 241301 (2014).
  34. M. Reig, On the high-scale instanton interference effect: Axion models without domain wall problem, J. High Energy Phys. 08 (2019) 167.
  35. Y. Zhang, Imperfect axion precludes the domain wall problem, Phys. Rev. Lett. 132, 081003 (2024).
  36. P. Minkowski, μ→eγ at a rate of one out of 109 muon decays?, Phys. Lett. 67B, 421 (1977).
  37. T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131, 95 (1979).
  38. M. Gell-Mann, P. Ramond, and R. Slansky, Complex spinors and unified theories, Conf. Proc. C 790927, 315 (1979).
  39. S. L. Glashow, The future of elementary particle physics, NATO Sci. Ser. B 61, 687 (1980).
  40. T. Yanagida, Horizontal symmetry and masses of neutrinos, Prog. Theor. Phys. 64, 1103 (1980).
  41. R. N. Mohapatra and G. Senjanović, Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett. 44, 912 (1980).
  42. R. Foot, H. Lew, X. G. He, and G. C. Joshi, Seesaw neutrino masses induced by a triplet of leptons, Z. Phys. C 44, 441 (1989).
  43. G. Lazarides, Q. Shafi, and C. Wetterich, Proton lifetime and fermion masses in an SO(10) model, Nucl. Phys. B181, 287 (1981).
  44. J. Schechter and J. W. F. Valle, Neutrino masses in SU(2)×U(1) theories, Phys. Rev. D 22, 2227 (1980).
  45. R. N. Mohapatra and G. Senjanovic, Neutrino masses and mixings in gauge models with spontaneous parity violation, Phys. Rev. D 23, 165 (1981).
  46. T. P. Cheng and L.-F. Li, Neutrino masses, mixings, and oscillations in SU(2)×U(1) models of electroweak interactions, Phys. Rev. D 22, 2860 (1980).
  47. C. Wetterich, Neutrino masses and the scale of B-L violation, Nucl. Phys. B187, 343 (1981).
  48. Y. Chikashige, R. N. Mohapatra, and R. D. Peccei, Spontaneously broken lepton number and cosmological constraints on the neutrino mass spectrum, Phys. Rev. Lett. 45, 1926 (1980).
  49. Y. Chikashige, R. N. Mohapatra, and R. D. Peccei, Are there real Goldstone bosons associated with broken lepton number?, Phys. Lett. B98, 265 (1981).
  50. G. B. Gelmini and M. Roncadelli, Left-handed neutrino mass scale and spontaneously broken lepton number, Phys. Lett. B99, 411 (1981).
  51. Z. G. Berezhiani, A. Y. Smirnov, and J. W. F. Valle, Observable Majoron emission in neutrinoless double beta decay, Phys. Lett. B 291, 99 (1992).
  52. J. Schechter and J. W. F. Valle, Neutrino decay and spontaneous violation of lepton number, Phys. Rev. D 25, 774 (1982).
  53. K. Choi, C. W. Kim, W. P. Lam, and A. Santamaria, Dark matter neutrinos and natural mass hierarchy in singlet—triplet Majoron model, Report No. CMU-HEP89-22, No. JHU-TIPAC-8912, and No. MPI-PAE-PTH-74-89 (1989).
  54. K. Choi and A. Santamaria, 17-KeV neutrino in a singlet—triplet Majoron model, Phys. Lett. B 267, 504 (1991).
  55. C. Garcia-Cely and J. Heeck, Neutrino lines from Majoron dark matter, J. High Energy Phys. 05 (2017) 102.
  56. T. Brune and H. Päs, Massive Majorons and constraints on the Majoron-neutrino coupling, Phys. Rev. D 99, 096005 (2019).
  57. J. Heeck and H. H. Patel, Majoron at two loops, Phys. Rev. D 100, 095015 (2019).
  58. M. Reig, J. W. F. Valle, and M. Yamada, Light Majoron cold dark matter from topological defects and the formation of boson stars, J. Cosmol. Astropart. Phys. 09 (2019) 029.
  59. K. Akita and M. Niibo, Updated constraints and future prospects on Majoron dark matter, J. High Energy Phys. 07 (2023) 132.
  60. A. Greljo, X. Ponce Díaz, and A. E. Thomsen, Insights on the cosmic origin of matter from proton stability, J. Cosmol. Astropart. Phys. 11 (2025) 043.
  61. G. Lazarides, M. Reig, Q. Shafi, R. Srivastava, and J. W. F. Valle, Spontaneous breaking of lepton number and the cosmological domain wall problem, Phys. Rev. Lett. 122, 151301 (2019).
  62. S. L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177, 2426 (1969).
  63. J. S. Bell and R. Jackiw, A PCAC puzzle: π0→γγ in the σ model, Nuovo Cimento Soc. Ital. Fis. 60A, 47 (1969).
  64. G. Lazarides and Q. Shafi, Axion models with no domain wall problem, Phys. Lett. B115, 21 (1982).
  65. S. M. Barr, D. B. Reiss, and A. Zee, Families, the invisible axion, and domain walls, Phys. Lett. B116, 227 (1982).
  66. T. Brune, Leptogenesis in Majoron models without domain walls, Phys. Rev. D 107, 096023 (2023).
  67. T. Brune, Leptogenesis in a Majoron+Triplet model, Phys. Rev. D 111, 115001 (2025).
  68. A. A. Anselm and A. A. Johansen, Baryon nonconservation in standard model and Yukawa interaction, Nucl. Phys. B407, 313 (1993).
  69. A. A. Anselm and A. A. Johansen, Can electroweak theta term be observable?, Nucl. Phys. B412, 553 (1994).
  70. G. Dvali, Three-form gauging of axion symmetries and gravity, arXiv:hep-th/0507215.
  71. P. Fileviez Perez and H. H. Patel, The electroweak vacuum angle, Phys. Lett. B 732, 241 (2014).
  72. A. J. Long, H. H. Patel, and M. Trodden, Electroweak vacuum angle at finite temperature and implications for baryogenesis, Phys. Rev. D 92, 043513 (2015).
  73. M. Shifman and A. Vainshtein, (In)dependence of Θ in the Higgs regime without axions, Mod. Phys. Lett. A 32, 1750084 (2017).
  74. J. Quevillon and C. Smith, Axions are blind to anomalies, Eur. Phys. J. C 79, 822 (2019).
  75. J. Quevillon and C. Smith, Baryon and lepton number intricacies in axion models, Phys. Rev. D 102, 075031 (2020).
  76. J. Quevillon and C. Smith, Variations on the SU(5) axion, Eur. Phys. J. Plus 137, 141 (2022).
  77. C. Csáki, R. T. D’Agnolo, E. Kuflik, and M. Ruhdorfer, Instanton NDA and applications to axion models, J. High Energy Phys. 04 (2024) 074.
  78. Y. Nomura, T. Watari, and T. Yanagida, Quintessence axion potential induced by electroweak instanton effects, Phys. Lett. B 484, 103 (2000).
  79. L. McLerran, R. Pisarski, and V. Skokov, Electroweak instantons, axions, and the cosmological constant, Phys. Lett. B 713, 301 (2012).
  80. M. Ibe, M. Yamazaki, and T. T. Yanagida, Quintessence axion revisited in light of swampland conjectures, Classical Quantum Gravity 36, 235020 (2019).
  81. G. Dvali, A. Kobakhidze, and O. Sakhelashvili, Electroweak ηw meson, Phys. Rev. D 111, 113002 (2025).
  82. H. K. Dreiner, H. E. Haber, and S. P. Martin, Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry, Phys. Rep. 494, 1 (2010).
  83. A. B. Beneito, I, J. Gargalionis, J. Herrero-Garcia, A. Santamaria, and M. A. Schmidt, An EFT approach to baryon number violation: lower limits on the new physics scale and correlations between nucleon decay modes, J. High Energy Phys. 07 (2024) 004.
  84. J. Gargalionis, J. Herrero-García, and M. A. Schmidt, Model-independent estimates for loop-induced baryon-number-violating nucleon decays, J. High Energy Phys. 06 (2024) 182.
  85. H. Georgi and S. L. Glashow, Unity of all elementary particle forces, Phys. Rev. Lett. 32, 438 (1974).
  86. P. Langacker, R. D. Peccei, and T. Yanagida, Invisible axions and light neutrinos: Are they connected?, Mod. Phys. Lett. A 01, 541 (1986).
  87. M. Shin, Light neutrino masses and strong CP problem, Phys. Rev. Lett. 59, 2515 (1987); 60, 383(E) (1988).
  88. G. Ballesteros, J. Redondo, A. Ringwald, and C. Tamarit, Unifying inflation with the axion, dark matter, baryogenesis and the seesaw mechanism, Phys. Rev. Lett. 118, 071802 (2017).
  89. G. Ballesteros, J. Redondo, A. Ringwald, and C. Tamarit, Standard model—axion—seesaw—Higgs portal inflation. Five problems of particle physics and cosmology solved in one stroke, J. Cosmol. Astropart. Phys. 08 (2017) 001.
  90. G. ’t Hooft, Symmetry breaking through Bell-Jackiw anomalies, Phys. Rev. Lett. 37, 8 (1976).
  91. G. ’t Hooft, Computation of the quantum effects due to a four-dimensional pseudoparticle, Phys. Rev. D 14, 3432 (1976); 18, 2199(E) (1978).
  92. I. Affleck, On constrained instantons, Nucl. Phys. B191, 429 (1981).
  93. J. Preskill, M. B. Wise, and F. Wilczek, Cosmology of the invisible axion, Phys. Lett. B120, 127 (1983).
  94. L. F. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. B120, 133 (1983).
  95. M. Dine and W. Fischler, The not so harmless axion, Phys. Lett. B120, 137 (1983).
  96. S. Koren, A note on proton stability in the standard model, Universe 8, 308 (2022).
  97. T. Hiramatsu, M. Kawasaki, and K. Saikawa, Evolution of string-wall networks and axionic domain wall problem, J. Cosmol. Astropart. Phys. 08 (2011) 030.
  98. G. Grilli di Cortona, E. Hardy, J. Pardo Vega, and G. Villadoro, The QCD axion, precisely, J. High Energy Phys. 01 (2016) 034.
  99. A. Friedland, H. Murayama, and M. Perelstein, Domain walls as dark energy, Phys. Rev. D 67, 043519 (2003).
  100. P. B. Arnold and L. D. McLerran, The sphaleron strikes back, Phys. Rev. D 37, 1020 (1988).
  101. L. D. McLerran, E. Mottola, and M. E. Shaposhnikov, Sphalerons and axion dynamics in high temperature QCD, Phys. Rev. D 43, 2027 (1991).
  102. H. M. Georgi, L. J. Hall, and M. B. Wise, Grand unified models with an automatic Peccei-Quinn symmetry, Nucl. Phys. B192, 409 (1981).
  103. M. Dine and N. Seiberg, String theory and the strong CP problem, Nucl. Phys. B273, 109 (1986).
  104. S. R. Coleman and K.-M. Lee, Wormholes made without massless matter fields, Nucl. Phys. B329, 387 (1990).
  105. L. F. Abbott and M. B. Wise, Wormholes and global symmetries, Nucl. Phys. B325, 687 (1989).
  106. R. Holman, S. D. H. Hsu, T. W. Kephart, E. W. Kolb, R. Watkins, and L. M. Widrow, Solutions to the strong CP problem in a world with gravity, Phys. Lett. B 282, 132 (1992).
  107. M. Kamionkowski and J. March-Russell, Planck scale physics and the Peccei-Quinn mechanism, Phys. Lett. B 282, 137 (1992).
  108. S. M. Barr and D. Seckel, Planck scale corrections to axion models, Phys. Rev. D 46, 539 (1992).
  109. S. Ghigna, M. Lusignoli, and M. Roncadelli, Instability of the invisible axion, Phys. Lett. B 283, 278 (1992).
  110. R. Kallosh, A. D. Linde, D. A. Linde, and L. Susskind, Gravity and global symmetries, Phys. Rev. D 52, 912 (1995).
  111. R. Alonso and A. Urbano, Wormholes and masses for Goldstone bosons, J. High Energy Phys. 02 (2019) 136.
  112. J. Preskill, S. P. Trivedi, F. Wilczek, and M. B. Wise, Cosmology and broken discrete symmetry, Nucl. Phys. B363, 207 (1991).
  113. C.-W. Chiang and B.-Q. Lu, Testing clockwork axion with gravitational waves, J. Cosmol. Astropart. Phys. 05 (2021) 049.
  114. N. Kitajima, J. Lee, K. Murai, F. Takahashi, and W. Yin, Gravitational waves from domain wall collapse, and application to nanohertz signals with QCD-coupled axions, Phys. Lett. B 851, 138586 (2024).
  115. Y. Bai, T.-K. Chen, and M. Korwar, QCD-collapsed domain walls: QCD phase transition and gravitational wave spectroscopy, J. High Energy Phys. 12 (2023) 194.
  116. S. Blasi, A. Mariotti, A. Rase, and A. Sevrin, Axionic domain walls at Pulsar Timing Arrays: QCD bias and particle friction, J. High Energy Phys. 11 (2023) 169.
  117. B.-Q. Lu, C.-W. Chiang, and T. Li, Clockwork axion footprint on nanohertz stochastic gravitational wave background, Phys. Rev. D 109, L101304 (2024).
  118. T. Hiramatsu, M. Kawasaki, and K. Saikawa, Gravitational waves from collapsing domain walls, J. Cosmol. Astropart. Phys. 05 (2010) 032.
  119. A. Eberhardt and E. G. M. Ferreira, Ultralight fuzzy dark matter review, arXiv:2507.00705.
  120. K. K. Rogers and H. V. Peiris, Strong bound on canonical ultralight axion dark matter from the Lyman-alpha forest, Phys. Rev. Lett. 126, 071302 (2021).
  121. M. J. Stott and D. J. E. Marsh, Black hole spin constraints on the mass spectrum and number of axionlike fields, Phys. Rev. D 98, 083006 (2018).
  122. M. Baryakhtar, L. Rosenberg, and G. Rybka, Searching for the QCD dark matter axion, arXiv:2504.10607.
  123. A. Arvanitaki, M. Baryakhtar, and X. Huang, Discovering the QCD axion with black holes and gravitational waves, Phys. Rev. D 91, 084011 (2015).
  124. A. Hook, Solving the hierarchy problem discretely, Phys. Rev. Lett. 120, 261802 (2018).
  125. L. Di Luzio, B. Gavela, P. Quilez, and A. Ringwald, An even lighter QCD axion, J. High Energy Phys. 05 (2021) 184.
  126. Q. Lu, M. Reece, and Z. Sun, The quality/cosmology tension for a post-inflation QCD axion, J. High Energy Phys. 07 (2024) 227.
  127. R. T. Co, T. Lee, and O. P. Leonard, (Non-)perturbative dynamics of a light QCD axion: Dark matter and the strong CP problem, Phys. Rev. D 112, 115007 (2025).
  128. J. N. Benabou, K. Fraser, M. Reig, and B. R. Safdi, String theory and grand unification suggest a submicroelectronvolt QCD axion, Phys. Rev. D 112, 066003 (2025).
  129. D. Jurčiukonis and L. Lavoura, On the addition of a large scalar multiplet to the standard model, Prog. Theor. Exp. Phys. 2024, 083B06 (2024).
  130. K. Hally, H. E. Logan, and T. Pilkington, Constraints on large scalar multiplets from perturbative unitarity, Phys. Rev. D 85, 095017 (2012).
  131. M. Cirelli, N. Fornengo, and A. Strumia, Minimal dark matter, Nucl. Phys. B753, 178 (2006).
  132. K. Choi and A. Santamaria, Majorons and supernova cooling, Phys. Rev. D 42, 293 (1990).
  133. T. Hiramatsu, M. Kawasaki, K. Saikawa, and T. Sekiguchi, Axion cosmology with long-lived domain walls, J. Cosmol. Astropart. Phys. 01 (2013) 001.
  134. Y. Fujii, Origin of the gravitational constant and particle masses in scale invariant scalar—tensor theory, Phys. Rev. D 26, 2580 (1982).
  135. L. H. Ford, Cosmological-constant damping by unstable scalar fields, Phys. Rev. D 35, 2339 (1987).
  136. C. Wetterich, Cosmology and the fate of dilatation symmetry, Nucl. Phys. B302, 668 (1988).
  137. B. Ratra and P. J. E. Peebles, Cosmological consequences of a rolling homogeneous scalar field, Phys. Rev. D 37, 3406 (1988).
  138. M. Fukugita and T. Yanagida, Model for the cosmological constant, Report No. YITP-K-1098 (1994).
  139. J. A. Frieman, C. T. Hill, A. Stebbins, and I. Waga, Cosmology with ultralight pseudo Nambu-Goldstone bosons, Phys. Rev. Lett. 75, 2077 (1995).
  140. K. Choi, String or M theory axion as a quintessence, Phys. Rev. D 62, 043509 (2000).
  141. J. E. Kim and H. P. Nilles, A quintessential axion, Phys. Lett. B 553, 1 (2003).
  142. L. J. Hall, Y. Nomura, and S. J. Oliver, Evolving dark energy with w deviating from −1, Phys. Rev. Lett. 95, 141302 (2005).
  143. R. Barbieri, L. J. Hall, S. J. Oliver, and A. Strumia, Dark energy and right-handed neutrinos, Phys. Lett. B 625, 189 (2005).
  144. https://www.overleaf.com/learn
  145. A. G. Adame et al. (DESI Collaboration), DESI 2024 VI: Cosmological constraints from the measurements of baryon acoustic oscillations, J. Cosmol. Astropart. Phys. 02 (2025) 021.
  146. R. Calderon et al. (DESI Collaboration), DESI 2024: Reconstructing dark energy using crossing statistics with DESI DR1 BAO data, J. Cosmol. Astropart. Phys. 10 (2024) 048.
  147. K. Lodha et al. (DESI Collaboration), DESI 2024: Constraints on physics-focused aspects of dark energy using DESI DR1 BAO data, Phys. Rev. D 111, 023532 (2025).
  148. M. Abdul Karim et al. (DESI Collaboration), DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraints, Phys. Rev. D 112, 083515 (2025).
  149. K. Lodha et al. (DESI Collaboration), Extended dark energy analysis using DESI DR2 BAO measurements, Phys. Rev. D 112, 083511 (2025).
  150. S. Dutta and R. J. Scherrer, Hilltop quintessence, Phys. Rev. D 78, 123525 (2008).
  151. Y. Tada and T. Terada, Quintessential interpretation of the evolving dark energy in light of DESI observations, Phys. Rev. D 109, L121305 (2024).
  152. S. Bhattacharya, G. Borghetto, A. Malhotra, S. Parameswaran, G. Tasinato, and I. Zavala, Cosmological tests of quintessence in quantum gravity, J. Cosmol. Astropart. Phys. 04 (2025) 086.
  153. M. Berbig, Kick it like DESI: PNGB quintessence with a dynamically generated initial velocity, J. Cosmol. Astropart. Phys. 03 (2025) 015.
  154. L. A. Ureña-López et al., Updated cosmological constraints on axion dark energy with DESI, Phys. Rev. D 112, 103505 (2025).
  155. W. Lin, L. Visinelli, and T. T. Yanagida, Testing quintessence axion dark energy with recent cosmological results, J. Cosmol. Astropart. Phys. 10 (2025) 023.
  156. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  157. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. V. CMB power spectra and likelihoods, Astron. Astrophys. 641, A5 (2020).
  158. F. J. Qu et al. (ACT Collaboration), The Atacama Cosmology Telescope: A measurement of the DR6 CMB lensing power spectrum and its implications for structure growth, Astrophys. J. 962, 112 (2024).
  159. M. S. Madhavacheril et al. (ACT Collaboration), The Atacama Cosmology Telescope: DR6 gravitational lensing map and cosmological parameters, Astrophys. J. 962, 113 (2024).
  160. D. Brout et al., The Pantheon+Analysis: Cosmological constraints, Astrophys. J. 938, 110 (2022).
  161. D. Rubin et al., Union through UNITY: Cosmology with 2,000 SNe using a unified Bayesian framework, Astrophys. J. 986, 231 (2025).
  162. T. M. C. Abbott et al. (DES Collaboration), The Dark Energy Survey: Cosmology results with ∼1500 new high-redshift type ia supernovae using the full 5 yr data set, Astrophys. J. Lett. 973, L14 (2024).
  163. N. Arkani-Hamed, L. Motl, A. Nicolis, and C. Vafa, The string landscape, black holes and gravity as the weakest force, J. High Energy Phys. 06 (2007) 060.
  164. H. Ooguri and C. Vafa, On the geometry of the string landscape and the swampland, Nucl. Phys. B766, 21 (2007).
  165. R. R. Caldwell, A phantom menace?, Phys. Lett. B 545, 23 (2002).
  166. R. R. Caldwell, M. Kamionkowski, and N. N. Weinberg, Phantom energy and cosmic doomsday, Phys. Rev. Lett. 91, 071301 (2003).
  167. I. D. Gialamas, G. Hütsi, K. Kannike, A. Racioppi, M. Raidal, M. Vasar, and H. Veermäe, Interpreting DESI 2024 BAO: Late-time dynamical dark energy or a local effect?, Phys. Rev. D 111, 043540 (2025).
  168. M. Chevallier and D. Polarski, Accelerating universes with scaling dark matter, Int. J. Mod. Phys. D 10, 213 (2001).
  169. E. V. Linder, Exploring the expansion history of the universe, Phys. Rev. Lett. 90, 091301 (2003).
  170. J. M. Cline, S. Jeon, and G. D. Moore, The Phantom menaced: Constraints on low-energy effective ghosts, Phys. Rev. D 70, 043543 (2004).
  171. K. J. Ludwick, The viability of phantom dark energy: A review, Mod. Phys. Lett. A 32, 1730025 (2017).
  172. G. Ye, M. Martinelli, B. Hu, and A. Silvestri, Hints of nonminimally coupled gravity in DESI 2024 baryon acoustic oscillation measurements, Phys. Rev. Lett. 134, 181002 (2025).
  173. W. J. Wolf, P. G. Ferreira, and C. García-García, Matching current observational constraints with nonminimally coupled dark energy, Phys. Rev. D 111, L041303 (2025).
  174. W. J. Wolf, C. García-García, T. Anton, and P. G. Ferreira, Assessing cosmological evidence for nonminimal coupling, Phys. Rev. Lett. 135, 081001 (2025).
  175. L. Amendola, Coupled quintessence, Phys. Rev. D 62, 043511 (2000).
  176. S. Das, P. S. Corasaniti, and J. Khoury, Super-acceleration as signature of dark sector interaction, Phys. Rev. D 73, 083509 (2006).
  177. J. Khoury, M.-X. Lin, and M. Trodden, Apparent ω;−1 and a lower S8 from dark axion and dark baryons interactions, Phys. Rev. Lett. 135, 181001 (2025).
  178. A. Bedroya, G. Obied, C. Vafa, and D. H. Wu, Evolving dark sector and the dark dimension scenario, arXiv:2507.03090.
  179. R. Liu, Y. Zhu, W. Hu, and V. Miranda, Phantom mirage from axion dark energy, arXiv:2510.14957.
  180. Y. Minami and E. Komatsu, New extraction of the cosmic birefringence from the Planck 2018 polarization data, Phys. Rev. Lett. 125, 221301 (2020).
  181. P. Diego-Palazuelos et al., Cosmic birefringence from the Planck data release 4, Phys. Rev. Lett. 128, 091302 (2022).
  182. J. R. Eskilt and E. Komatsu, Improved constraints on cosmic birefringence from the WMAP and Planck cosmic microwave background polarization data, Phys. Rev. D 106, 063503 (2022).
  183. T. Louis et al. (ACT Collaboration), The Atacama Cosmology Telescope: DR6 power spectra, likelihoods and ΛCDM parameters, J. Cosmol. Astropart. Phys. 11 (2025) 062.
  184. M. Bauer, M. Neubert, and A. Thamm, Collider probes of axion-like particles, J. High Energy Phys. 12 (2017) 044.

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Phys. Rev. D 113, 043515– Published 13 February, 2026
  • Received 21 July 2025
  • Accepted 23 January 2026
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