- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

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

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Inflationary QCD phase diagram

Kohei Fujikura1,* and Toshifumi Noumi2,†

  • *Contact author: kohei.fujikura@yukawa.kyoto-u.ac.jp
  • †Contact author: tnoumi@g.ecc.u-tokyo.ac.jp
PDF

Phys. Rev. D 113, 123543 – Published 23 June, 2026

DOI: https://doi.org/10.1103/3ljp-ddfx

Abstract

Motivated by the cosmological collider program, which aims to probe high-energy physics through inflation, we investigate the phase diagram of multiflavor QCD in de Sitter spacetime with a flavor-universal axial chemical potential induced by a rolling inflaton coupled to fermions. We determine the first-order critical line and a critical point as functions of the Hubble parameter and the axial chemical potential, employing an effective description of chiral symmetry breaking within the framework of the Nambu–Jona-Lasinio model. We find that a first-order chiral phase transition may occur during inflation or at its end when the axial chemical potential is sufficiently large and crosses the critical line. This serves as a benchmark cosmological analog of the QCD phase diagram explored in heavy-ion colliders.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (60)

  1. A. A. Starobinsky, A new type of isotropic cosmological models without singularity, Phys. Lett. 91B, 99 (1980).
  2. A. H. Guth, The inflationary universe: A possible solution to the horizon and flatness problems, Phys. Rev. D 23, 347 (1981).
  3. K. Sato, First-order phase transition of a vacuum and the expansion of the universe, Mon. Not. R. Astron. Soc. 195, 467 (1981).
  4. E. Komatsu, K. M. Smith, J. Dunkley, C. L. Bennett, B. Gold, G. Hinshaw et al., Seven-year Wilkinson microwave anisotropy probe (WMAP) observations: Cosmological interpretation, Astrophys. J. Suppl. Ser. 192, 18 (2011).
  5. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020).
  6. X. Chen and Y. Wang, Quasi-single field inflation and non-gaussianities, J. Cosmol. Astropart. Phys. 04 (2010) 027.
  7. D. Baumann and D. Green, Signatures of supersymmetry from the early universe, Phys. Rev. D 85, 103520 (2012).
  8. T. Noumi, M. Yamaguchi, and D. Yokoyama, Effective field theory approach to quasi-single field inflation and effects of heavy fields, J. High Energy Phys. 06 (2013) 051.
  9. N. Arkani-Hamed and J. Maldacena, Cosmological collider physics, arXiv:1503.08043.
  10. J. M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, J. High Energy Phys. 05 (2003) 013.
  11. V. Acquaviva, N. Bartolo, S. Matarrese, and A. Riotto, Second order cosmological perturbations from inflation, Nucl. Phys. B667, 119 (2003).
  12. G. W. Gibbons and S. W. Hawking, Cosmological event horizons, thermodynamics, and particle creation, Phys. Rev. D 15, 2738 (1977).
  13. A. G. Cohen and D. B. Kaplan, Thermodynamic generation of the baryon asymmetry, Phys. Lett. B 199, 251 (1987).
  14. A. G. Cohen and D. B. Kaplan, Spontaneous baryogenesis, Nucl. Phys. B308, 913 (1988).
  15. P. Adshead and E. I. Sfakianakis, Fermion production during and after axion inflation, J. Cosmol. Astropart. Phys. 11 (2015) 021.
  16. R. Flauger, M. Mirbabayi, L. Senatore, and E. Silverstein, Productive interactions: Heavy particles and non-Gaussianity, J. Cosmol. Astropart. Phys. 10 (2017) 058.
  17. P. Adshead, L. Pearce, M. Peloso, M. A. Roberts, and L. Sorbo, Phenomenology of fermion production during axion inflation, J. Cosmol. Astropart. Phys. 06 (2018) 020.
  18. X. Chen, Y. Wang, and Z.-Z. Xianyu, Neutrino signatures in primordial non-Gaussianities, J. High Energy Phys. 09 (2018) 022.
  19. V. Domcke and K. Mukaida, Gauge field and fermion production during axion inflation, J. Cosmol. Astropart. Phys. 11 (2018) 020.
  20. A. Hook, J. Huang, and D. Racco, Searches for other vacua. Part II. A new Higgstory at the cosmological collider, J. High Energy Phys. 01 (2020) 105.
  21. L.-T. Wang and Z.-Z. Xianyu, In search of large signals at the cosmological collider, J. High Energy Phys. 02 (2020) 044.
  22. A. Bodas, S. Kumar, and R. Sundrum, The scalar chemical potential in cosmological collider physics, J. High Energy Phys. 02 (2021) 079.
  23. X. Tong, Y. Wang, C. Zhang, and Y. Zhu, BCS in the sky: Signatures of inflationary fermion condensation, J. Cosmol. Astropart. Phys. 04 (2024) 022.
  24. A. Bodas, E. Broadberry, R. Sundrum, and Z. Xu, Charged loops at the cosmological collider with chemical potential, J. High Energy Phys. 01 (2026) 083.
  25. L. D. McLerran, E. Mottola, and M. E. Shaposhnikov, Sphalerons and axion dynamics in high temperature QCD, Phys. Rev. D 43, 2027 (1991).
  26. L. Yu, H. Liu, and M. Huang, Effect of the chiral chemical potential on the chiral phase transition in the NJL model with different regularization schemes, Phys. Rev. D 94, 014026 (2016).
  27. R. L. S. Farias, D. C. Duarte, G. a. Krein, and R. O. Ramos, Thermodynamics of quark matter with a chiral imbalance, Phys. Rev. D 94, 074011 (2016).
  28. Y. Lu, Z.-F. Cui, Z. Pan, C.-H. Chang, and H.-S. Zong, QCD phase diagram with a chiral chemical potential, Phys. Rev. D 93, 074037 (2016).
  29. T. G. Khunjua, K. G. Klimenko, and R. N. Zhokhov, Chiral imbalanced hot and dense quark matter: NJL analysis at the physical point and comparison with lattice QCD, Eur. Phys. J. C 79, 151 (2019).
  30. L.-K. Yang, X. Luo, and H.-S. Zong, QCD phase diagram in chiral imbalance with self-consistent mean field approximation, Phys. Rev. D 100, 094012 (2019).
  31. K. Fukushima, M. Ruggieri, and R. Gatto, Chiral magnetic effect in the PNJL model, Phys. Rev. D 81, 114031 (2010).
  32. R. Gatto and M. Ruggieri, Hot quark matter with an axial chemical potential, Phys. Rev. D 85, 054013 (2012).
  33. Z.-F. Cui, I. C. Cloet, Y. Lu, C. D. Roberts, S. M. Schmidt, S.-S. Xu, and H.-S. Zong, Critical endpoint in the presence of a chiral chemical potential, Phys. Rev. D 94, 071503 (2016).
  34. F. X. Azeredo, D. C. Duarte, R. L. S. Farias, G. a. Krein, and R. O. Ramos, Deconfinement and chiral phase transitions in quark matter with chiral imbalance, Phys. Rev. D 110, 076007 (2024).
  35. M. N. Chernodub and A. S. Nedelin, Phase diagram of chirally imbalanced QCD matter, Phys. Rev. D 83, 105008 (2011).
  36. S.-S. Xu, Z.-F. Cui, B. Wang, Y.-M. Shi, Y.-C. Yang, and H.-S. Zong, Chiral phase transition with a chiral chemical potential in the framework of Dyson-Schwinger equations, Phys. Rev. D 91, 056003 (2015).
  37. B. Wang, Y.-L. Wang, Z.-F. Cui, and H.-S. Zong, Effect of the chiral chemical potential on the position of the critical endpoint, Phys. Rev. D 91, 034017 (2015).
  38. V. V. Braguta, V. A. Goy, E. M. Ilgenfritz, A. Y. Kotov, A. V. Molochkov, M. Muller-Preussker, and B. Petersson, Two-color QCD with non-zero chiral chemical potential, J. High Energy Phys. 06 (2015) 094.
  39. V. V. Braguta, E. M. Ilgenfritz, A. Y. Kotov, B. Petersson, and S. A. Skinderev, Study of QCD phase diagram with non-zero chiral chemical potential, Phys. Rev. D 93, 034509 (2016).
  40. Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. 1, Phys. Rev. 122, 345 (1961).
  41. Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. II, Phys. Rev. 124, 246 (1961).
  42. T. Hatsuda and T. Kunihiro, QCD phenomenology based on a chiral effective Lagrangian, Phys. Rep. 247, 221 (1994).
  43. T. Inagaki, T. Muta, and S. D. Odintsov, Dynamical symmetry breaking in curved space-time: Four fermion interactions, Prog. Theor. Phys. Suppl. 127, 93 (1997).
  44. M. Kobayashi and T. Maskawa, Chiral symmetry and eta-x mixing, Prog. Theor. Phys. 44, 1422 (1970).
  45. M. Kobayashi, H. Kondo, and T. Maskawa, Symmetry breaking of the chiral U(3)⊗U(3) and the quark model, Prog. Theor. Phys. 45, 1955 (1971).
  46. G. ’t Hooft, Computation of the quantum effects due to a four-dimensional pseudoparticle, Phys. Rev. D 14, 3432 (1976).
  47. G. ’t Hooft, How instantons solve the U(1) problem, Phys. Rep. 142, 357 (1986).
  48. M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, QCD and resonance physics. Theoretical foundations, Nucl. Phys. B147, 385 (1979).
  49. G. ’t Hooft, Symmetry breaking through Bell-Jackiw anomalies, Phys. Rev. Lett. 37, 8 (1976).
  50. D. J. Gross, R. D. Pisarski, and L. G. Yaffe, QCD and instantons at finite temperature, Rev. Mod. Phys. 53, 43 (1981).
  51. H. Reinhardt and R. Alkofer, Instanton induced flavor mixing in mesons, Phys. Lett. B 207, 482 (1988).
  52. D. Ebert and H. Reinhardt, Effective chiral hadron Lagrangian with anomalies and skyrme terms from quark flavour dynamics, Nucl. Phys. B271, 188 (1986).
  53. K. Fukushima, Phase diagrams in the three-flavor Nambu-Jona-Lasinio model with the Polyakov loop, Phys. Rev. D 77, 114028 (2008).
  54. P. Adshead, J. T. Giblin, T. R. Scully, and E. I. Sfakianakis, Magnetogenesis from axion inflation, J. Cosmol. Astropart. Phys. 10 (2016) 039.
  55. D. Green, M. Lewandowski, L. Senatore, E. Silverstein, and M. Zaldarriaga, Anomalous dimensions and non-gaussianity, J. High Energy Phys. 10 (2013) 171.
  56. M. Baumgart, J. J. Heckman, and L. Thomas, CFTs blueshift tensor fluctuations universally, J. Cosmol. Astropart. Phys. 07 (2022) 034.
  57. G. L. Pimentel and C. Yang, Strongly coupled sectors in inflation: Gapless theories and unparticles, J. High Energy Phys. 04 (2026) 146.
  58. C. Yang, Dark walker in the early universe: A strongly coupled sector model, Phys. Lett. B 872, 140073 (2026).
  59. O. H. E. Philcox, G. L. Pimentel, and C. Yang, Searching for unparticles with the cosmic microwave background, arXiv:2603.13486.
  60. P. Collas and D. Klein, The Dirac Equation in Curved Spacetime: A Guide for Calculations, SpringerBriefs in Physics (Springer, New York, 2019), 10.1007/978-3-030-14825-6.

Outline

Information

Phys. Rev. D 113, 123543– Published 23 June, 2026
  • Received 10 January 2026
  • Accepted 11 May 2026
Crossmark - Check for updates button
Creative Commons Logo

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

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation