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ACT-Planck data and phase transitions from a viable no-scale Standard Model completion

Filippo Cutrona, Francesco Rescigno, and Alberto Salvio

Phys. Rev. D 114, 043513 – Published 10 August, 2026

DOI: https://doi.org/10.1103/38mz-pw8t

Abstract

Classically scale-invariant (and perturbative) theories provide a way to understand large hierarchies, as scales are generated through dimensional transmutation. They always lead to first-order phase transitions, since symmetries are radiatively broken, and they generically feature quasiflat potentials, which are suitable for inflation. We construct a simple but fully realistic model of this kind that accounts for all observational evidence of new physics and is remarkably compatible with the most recent constraints on inflationary observables from both the Planck/BICEP/Keck and the Atacama Cosmology Telescope Collaborations. This model illustrates how classical scale invariance generically leads to a nonstandard cosmology in which inflation occurs in two stages: a slow-roll stage and a thermal stage, separated by a radiation-dominated era.

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References (69)

  1. S. Weinberg, Gauge and global symmetries at high temperature, Phys. Rev. D 9, 3357 (1974).
  2. M. Maggiore, Gravitational Waves. Vol. 2: Astrophysics and Cosmology (Oxford University Press, New York, 2018), 3.
  3. E. Gildener and S. Weinberg, Symmetry breaking and scalar bosons, Phys. Rev. D 13, 3333 (1976).
  4. A. Salvio, Inflationary scenarios beyond the standard model, in Encyclopedia of Particle Physics, 1st ed. (Elsevier, New York, 2025).
  5. S. R. Coleman and E. J. Weinberg, Radiative corrections as the origin of spontaneous symmetry breaking, Phys. Rev. D 7, 1888 (1973).
  6. A. Salvio, Model-independent radiative symmetry breaking and gravitational waves, J. Cosmol. Astropart. Phys. 04 (2023) 051.
  7. A. Salvio, Supercooled phase transitions with radiative symmetry breaking, Int. J. Mod. Phys. A 2646004, (2026).
  8. G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, NATO Sci. Ser. B 59, 135 (1980).
  9. D. M. Ghilencea and H. M. Lee, Weyl gauge symmetry and its spontaneous breaking in the standard model and inflation, Phys. Rev. D 99, 115007 (2019).
  10. T. Louis et al. (ACT Collaboration), The Atacama Cosmology Telescope: DR6 power spectra, likelihoods and ΛCDM parameters, J. Cosmol. Astropart. Phys. 11 (2025) 062.
  11. E. Calabrese et al. (ACT Collaboration), The Atacama Cosmology Telescope: DR6 constraints on extended cosmological models, J. Cosmol. Astropart. Phys. 11 (2025) 063.
  12. P. A. R. Ade et al. (Planck Collaboration), Planck 2015 results. XX. Constraints on inflation, Astron. Astrophys. 594, A20 (2016); Y. Akrami et al. (Planck Collaboration), Planck 2018 results. X. Constraints on inflation, 641, A10 (2020).
  13. P. A. R. Ade et al. (BICEP and Keck Collaboration), Improved constraints on primordial gravitational waves using Planck, WMAP, and BICEP/Keck observations through the 2018 observing season, Phys. Rev. Lett. 127, 151301 (2021).
  14. A. G. Adame et al. (DESI Collaboration), DESI 2024 III: Baryon acoustic oscillations from galaxies and quasars, J. Cosmol. Astropart. Phys. 04 (2025) 012; DESI 2024 VI: Cosmological constraints from the measurements of baryon acoustic oscillations, J. Cosmol. Astropart. Phys. 02 (2025) 021.
  15. K. Kannike, A. Racioppi, and M. Raidal, Embedding inflation into the standard model—more evidence for classical scale invariance, J. High Energy Phys. 06 (2014) 154.
  16. L. Marzola, A. Racioppi, M. Raidal, F. R. Urban, and H. Veermäe, Non-minimal CW inflation, electroweak symmetry breaking and the 750 GeV anomaly, J. High Energy Phys. 03 (2016) 190.
  17. L. Marzola and A. Racioppi, Minimal but non-minimal inflation and electroweak symmetry breaking, J. Cosmol. Astropart. Phys. 10 (2016) 010.
  18. I. D. Gialamas, A. Karam, A. Racioppi, and M. Raidal, Has ACT measured radiative corrections to the tree-level Higgs-like inflation?, Phys. Rev. D 112, 103544 (2025).
  19. For other ways to use scale invariance and its quantum breaking to account for the ACT results see: A. Salvio, Independent connection in action during inflation, Phys. Rev. D 112, L061301 (2025); Inflating and reheating the Universe with an independent affine connection, 106, 103510 (2022); J. Yuennan, P. Koad, F. Atamurotov, and P. Channuie, Quantum-corrected ϕ4 inflation in light of ACT observations, Eur. Phys. J. C 85, 1307 (2025).
  20. For early works fitting the ACT constraints without using CSI theories, see for example the following works. R. Kallosh, A. Linde, and D. Roest, Atacama Cosmology Telescope, South Pole Telescope, and chaotic inflation, Phys. Rev. Lett. 135, 161001 (2025); I. Antoniadis, J. Ellis, W. Ke, D. V. Nanopoulos, and K. A. Olive, How accidental was inflation?, J. Cosmol. Astropart. Phys. 08 (2025) 090.
  21. E. Witten, Cosmological consequences of a light Higgs boson, Nucl. Phys. B177, 477 (1981).
  22. J. Liu, L. Bian, R. G. Cai, Z. K. Guo, and S. J. Wang, Primordial black hole production during first-order phase transitions, Phys. Rev. D 105, L021303 (2022).
  23. Y. Gouttenoire and T. Volansky, Primordial black holes from supercooled phase transitions, Phys. Rev. D 110, 043514 (2024).
  24. A. Salvio, Supercooling in radiative symmetry breaking: Theory extensions, gravitational wave detection and primordial black holes, J. Cosmol. Astropart. Phys. 12 (2023) 046.
  25. Y. Gouttenoire, Primordial black holes from conformal Higgs, Phys. Lett. B 855, 138800 (2024).
  26. A. Salvio, Pulsar timing arrays and primordial black holes from a supercooled phase transition, Phys. Lett. B 852, 138639 (2024).
  27. M. Arteaga, A. Ghoshal, and A. Strumia, Gravitational waves and black holes from the phase transition in models of dynamical symmetry breaking, J. Cosmol. Astropart. Phys. 05 (2025) 029.
  28. Z. Ning, X. X. Zeng, R. G. Cai, and S. J. Wang, Numerical simulations of primordial black hole formation via delayed first-order phase transitions, arXiv:2601.21878.
  29. T. Asaka and M. Shaposhnikov, The nuMSM, dark matter and baryon asymmetry of the universe, Phys. Lett. B 620, 17 (2005).
  30. L. Canetti, M. Drewes, T. Frossard, and M. Shaposhnikov, Dark matter, baryogenesis and neutrino oscillations from right handed neutrinos, Phys. Rev. D 87, 093006 (2013).
  31. A. R. Liddle and S. M. Leach, How long before the end of inflation were observable perturbations produced?, Phys. Rev. D 68, 103503 (2003).
  32. S. Weinberg, Cosmology (Oxford University Press, Oxford, 2008).
  33. Greek indices are lowered and raised by the metric gμν, for which the mostly minus convention is assumed here. Fermions are represented by Weyl spinors.
  34. S. Iso, N. Okada, and Y. Orikasa, Classically conformal B−L extended Standard Model, Phys. Lett. B 676, 81 (2009).
  35. We use a compact notation where ϕ is an array of real scalars, which includes all scalars of the theory.
  36. A. Salvio and A. Strumia, Agravity, J. High Energy Phys. 06 (2014) 080.
  37. K. Kannike, G. Hütsi, L. Pizza, A. Racioppi, M. Raidal, A. Salvio, and A. Strumia, Dynamically induced Planck scale and inflation, J. High Energy Phys. 05 (2015) 065.
  38. A. Salvio and A. Strumia, Agravity up to infinite energy, Eur. Phys. J. C 78, 124 (2018).
  39. A. Salvio, Dimensional transmutation in gravity and cosmology, Int. J. Mod. Phys. A 36, 2130006 (2021).
  40. C. Álvarez-Luna, S. de la Calle-Leal, J. A. R. Cembranos, and J. J. Sanz-Cillero, Gravitational Coleman-Weinberg mechanism, J. High Energy Phys. 02 (2023) 232.
  41. C. Cecchini, M. De Angelis, W. Giarè, M. Rinaldi, and S. Vagnozzi, Testing scale-invariant inflation against cosmological data, J. Cosmol. Astropart. Phys. 07 (2024) 058.
  42. D. Anselmi, On the quantum field theory of the gravitational interactions, J. High Energy Phys. 06 (2017) 086.
  43. D. Anselmi and M. Piva, The ultraviolet behavior of quantum gravity, J. High Energy Phys. 05 (2018) 027.
  44. J. F. Donoghue and G. Menezes, Unitarity, stability and loops of unstable ghosts, Phys. Rev. D 100, 105006 (2019).
  45. A. Salvio, A non-perturbative and background-independent formulation of quadratic gravity, J. Cosmol. Astropart. Phys. 07 (2024) 092.
  46. A. Salvio, BICEP/Keck data and quadratic gravity, J. Cosmol. Astropart. Phys. 09 (2022) 027.
  47. D. Buttazzo, G. Degrassi, P. P. Giardino, G. F. Giudice, F. Sala, A. Salvio, and A. Strumia, Investigating the near-criticality of the Higgs boson, J. High Energy Phys. 12 (2013) 089.
  48. A. Joti, A. Katsis, D. Loupas, A. Salvio, A. Strumia, N. Tetradis, and A. Urbano, (Higgs) vacuum decay during inflation, J. High Energy Phys. 07 (2017) 058.
  49. A. Rajantie and S. Stopyra, Standard model vacuum decay in a de Sitter background, Phys. Rev. D 97, 025012 (2018).
  50. T. Markkanen, A. Rajantie, and S. Stopyra, Cosmological aspects of Higgs vacuum metastability, Front. Astron. Space Sci. 5, 40 (2018).
  51. E. Allys et al. (LiteBIRD Collaboration), Probing cosmic inflation with the LiteBIRD cosmic microwave background polarization survey, Prog. Theor. Exp. Phys. 2023, 042F01 (2023).
  52. K. N. Abazajian et al. (CMB-S4 Collaboration), CMB-S4 science book, first edition, arXiv:1610.02743.
  53. J. L. Cervantes-Cota and H. Dehnen, Induced gravity inflation in the standard model of particle physics, Nucl. Phys. B442, 391 (1995).
  54. F. L. Bezrukov and M. Shaposhnikov, The standard model Higgs boson as the inflaton, Phys. Lett. B 659, 703 (2008).
  55. C. P. Burgess, H. M. Lee, and M. Trott, Power-counting and the validity of the classical approximation during inflation, J. High Energy Phys. 09 (2009) 103.
  56. J. L. F. Barbon and J. R. Espinosa, On the naturalness of Higgs inflation, Phys. Rev. D 79, 081302 (2009).
  57. C. P. Burgess, H. M. Lee, and M. Trott, Comment on Higgs inflation and naturalness, J. High Energy Phys. 07 (2010) 007.
  58. M. P. Hertzberg, On inflation with non-minimal coupling, J. High Energy Phys. 11 (2010) 023.
  59. C. P. Burgess, S. P. Patil, and M. Trott, On the predictiveness of single-field inflationary models, J. High Energy Phys. 06 (2014) 010.
  60. F. Bezrukov, A. Magnin, M. Shaposhnikov, and S. Sibiryakov, Higgs inflation: Consistency and generalisations, J. High Energy Phys. 01 (2011) 016.
  61. A. Berera, Warm inflation, Phys. Rev. Lett. 75, 3218 (1995).
  62. S. Weinberg, The Quantum Theory of Fields. Vol. 2: Modern Applications, SPIRES entry (Cambridge University Press, Cambridge, England, (1996), p. 489. This reference considered the zero-temperature case, but one can easily obtain the same conclusion in the finite-temperature case by repeating the argument of this reference in Euclidean space and imposing periodic boundary conditions on the imaginary time.
  63. I. K. Banerjee, F. Rescigno, and A. Salvio, Primordial black holes (as dark matter) from the supercooled phase transitions with radiative symmetry breaking, J. Cosmol. Astropart. Phys. 07 (2025) 007.
  64. S. Babak, A. Petiteau, and M. Hewitson, LISA sensitivity and SNR calculations, arXiv:2108.01167.
  65. F. Rescigno and A. Salvio, Reheating after the supercooled phase transitions with radiative symmetry breaking, J. Cosmol. Astropart. Phys. 02 (2026) 021.
  66. A. Ghoshal and A. Salvio, Gravitational waves from fundamental axion dynamics, J. High Energy Phys. 12 (2020) 049.
  67. G. D’Amico and N. Kaloper, Rollercoaster cosmology, J. Cosmol. Astropart. Phys. 08 (2021) 058.
  68. M. E. Machacek and M. T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 1. Wave function renormalization, Nucl. Phys. B222, 83 (1983); Two loop renormalization group equations in a general quantum field theory. 2. Yukawa Couplings, B236, 221 (1984); Two loop renormalization group equations in a general quantum field theory. 3. Scalar quartic couplings, B249, 70 (1985).
  69. D. C. Youla, A normal form for a matrix under the unitary congruence group, Can. J. Math. 13, 694 (1961).

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