Abstract
It is difficult to construct a post-inflation QCD axion model that solves the axion quality problem (and hence the Strong CP problem) without introducing a cosmological disaster. In a post-inflation axion model, the axion field value is randomized during the Peccei-Quinn phase transition, and axion domain walls form at the QCD phase transition. We emphasize that the gauge equivalence of all minima of the axion potential (i.e., domain wall number equals one) is insufficient to solve the cosmological domain wall problem. The axion string on which a domain wall ends must exist as an individual object (as opposed to a multi-string state), and it must be produced in the early universe. These conditions are often not satisfied in concrete models. Post-inflation axion models also face a potential problem from fractionally charged relics; solving this problem often leads to low-energy Landau poles for Standard Model gauge couplings, reintroducing the quality problem. We study several examples, finding that models that solve the quality problem face cosmological problems, and vice versa. This is not a no-go theorem; nonetheless, we argue that it is much more difficult than generally appreciated to find a viable post-inflation QCD axion model. Successful examples may have a nonstandard cosmological history (e.g., multiple types of cosmic axion strings of different tensions), undermining the widespread expectation that the post-inflation QCD axion scenario predicts a unique mass for axion dark matter.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R.D. Peccei and H.R. Quinn, Constraints Imposed by CP Conservation in the Presence of Instantons, Phys. Rev. D 16 (1977) 1791 [INSPIRE].
R.D. Peccei and H.R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].
S. Weinberg, A New Light Boson?, Phys. Rev. Lett. 40 (1978) 223 [INSPIRE].
F. Wilczek, Problem of Strong P and T Invariance in the Presence of Instantons, Phys. Rev. Lett. 40 (1978) 279 [INSPIRE].
J. Preskill, M.B. Wise and F. Wilczek, Cosmology of the Invisible Axion, Phys. Lett. B 120 (1983) 127 [INSPIRE].
M. Dine and W. Fischler, The Not So Harmless Axion, Phys. Lett. B 120 (1983) 137 [INSPIRE].
L.F. Abbott and P. Sikivie, A Cosmological Bound on the Invisible Axion, Phys. Lett. B 120 (1983) 133 [INSPIRE].
J.E. Kim and G. Carosi, Axions and the Strong CP Problem, Rev. Mod. Phys. 82 (2010) 557 [Erratum ibid. 91 (2019) 049902] [arXiv:0807.3125] [INSPIRE].
A. Hook, TASI Lectures on the Strong CP Problem and Axions, PoS TASI2018 (2019) 004 [arXiv:1812.02669] [INSPIRE].
M. Reece, TASI Lectures: (No) Global Symmetries to Axion Physics, PoS TASI2022 (2024) 008 [arXiv:2304.08512] [INSPIRE].
M. Kawasaki and K. Nakayama, Axions: Theory and Cosmological Role, Ann. Rev. Nucl. Part. Sci. 63 (2013) 69 [arXiv:1301.1123] [INSPIRE].
D.J.E. Marsh, Axion Cosmology, Phys. Rept. 643 (2016) 1 [arXiv:1510.07633] [INSPIRE].
B.R. Safdi, TASI Lectures on the Particle Physics and Astrophysics of Dark Matter, PoS TASI2022 (2024) 009 [arXiv:2303.02169] [INSPIRE].
H.M. Georgi, L.J. Hall and M.B. Wise, Grand Unified Models With an Automatic Peccei-Quinn Symmetry, Nucl. Phys. B 192 (1981) 409 [INSPIRE].
G. Lazarides, C. Panagiotakopoulos and Q. Shafi, Phenomenology and Cosmology With Superstrings, Phys. Rev. Lett. 56 (1986) 432 [INSPIRE].
J.A. Casas and G.G. Ross, A Solution to the Strong CP Problem in Superstring Models, Phys. Lett. B 192 (1987) 119 [INSPIRE].
M. Kamionkowski and J. March-Russell, Planck scale physics and the Peccei-Quinn mechanism, Phys. Lett. B 282 (1992) 137 [hep-th/9202003] [INSPIRE].
R. Holman et al., Solutions to the strong CP problem in a world with gravity, Phys. Lett. B 282 (1992) 132 [hep-ph/9203206] [INSPIRE].
S.M. Barr and D. Seckel, Planck scale corrections to axion models, Phys. Rev. D 46 (1992) 539 [INSPIRE].
S. Ghigna, M. Lusignoli and M. Roncadelli, Instability of the invisible axion, Phys. Lett. B 283 (1992) 278 [INSPIRE].
L. Randall, Composite axion models and Planck scale physics, Phys. Lett. B 284 (1992) 77 [INSPIRE].
M. Dine, Problems of naturalness: Some lessons from string theory, in the proceedings of the Conference on Topics in Quantum Gravity, Cincinnati, U.S.A. (1992) [hep-th/9207045] [INSPIRE].
R. Kallosh, A.D. Linde, D.A. Linde and L. Susskind, Gravity and global symmetries, Phys. Rev. D 52 (1995) 912 [hep-th/9502069] [INSPIRE].
R. Contino, A. Podo and F. Revello, Chiral models of composite axions and accidental Peccei-Quinn symmetry, JHEP 04 (2022) 180 [arXiv:2112.09635] [INSPIRE].
Q. Bonnefoy, Heavy fields and the axion quality problem, Phys. Rev. D 108 (2023) 035023 [arXiv:2212.00102] [INSPIRE].
M. Redi and A. Tesi, Meso-inflationary QCD axion, Phys. Rev. D 107 (2023) 095032 [arXiv:2211.06421] [INSPIRE].
M. Gorghetto et al., Early vs late string networks from a minimal QCD Axion, JHEP 02 (2024) 223 [arXiv:2311.09315] [INSPIRE].
E. Witten, Some Properties of O(32) Superstrings, Phys. Lett. B 149 (1984) 351 [INSPIRE].
K.-W. Choi, A QCD axion from higher dimensional gauge field, Phys. Rev. Lett. 92 (2004) 101602 [hep-ph/0308024] [INSPIRE].
P. Svrcek and E. Witten, Axions In String Theory, JHEP 06 (2006) 051 [hep-th/0605206] [INSPIRE].
J.P. Conlon, The QCD axion and moduli stabilisation, JHEP 05 (2006) 078 [hep-th/0602233] [INSPIRE].
M. Cicoli, A. Hebecker, J. Jaeckel and M. Wittner, Axions in string theory — slaying the Hydra of dark radiation, JHEP 09 (2022) 198 [arXiv:2203.08833] [INSPIRE].
J.N. Benabou et al., The Cosmological Dynamics of String Theory Axion Strings, arXiv:2312.08425 [INSPIRE].
T. Asaka and M. Yamaguchi, Hadronic axion model in gauge mediated supersymmetry breaking, Phys. Lett. B 437 (1998) 51 [hep-ph/9805449] [INSPIRE].
T. Banks, M. Dine and M. Graesser, Supersymmetry, axions and cosmology, Phys. Rev. D 68 (2003) 075011 [hep-ph/0210256] [INSPIRE].
M.P. Hertzberg, M. Tegmark and F. Wilczek, Axion Cosmology and the Energy Scale of Inflation, Phys. Rev. D 78 (2008) 083507 [arXiv:0807.1726] [INSPIRE].
Y. Bao, J.J. Fan and L. Li, Opening up a Window on the Postinflationary QCD Axion, Phys. Rev. Lett. 130 (2023) 241001 [arXiv:2209.09908] [INSPIRE].
P. Sikivie, Of Axions, Domain Walls and the Early Universe, Phys. Rev. Lett. 48 (1982) 1156 [INSPIRE].
Y.B. Zeldovich, I.Y. Kobzarev and L.B. Okun, Cosmological Consequences of the Spontaneous Breakdown of Discrete Symmetry, Zh. Eksp. Teor. Fiz. 67 (1974) 3 [INSPIRE].
T.W.B. Kibble, G. Lazarides and Q. Shafi, Strings in SO(10), Phys. Lett. B 113 (1982) 237 [INSPIRE].
A. Vilenkin and A.E. Everett, Cosmic Strings and Domain Walls in Models with Goldstone and PseudoGoldstone Bosons, Phys. Rev. Lett. 48 (1982) 1867 [INSPIRE].
T.W.B. Kibble, G. Lazarides and Q. Shafi, Walls Bounded by Strings, Phys. Rev. D 26 (1982) 435 [INSPIRE].
A.E. Everett and A. Vilenkin, Left-right Symmetric Theories and Vacuum Domain Walls and Strings, Nucl. Phys. B 207 (1982) 43 [INSPIRE].
G.B. Gelmini, M. Gleiser and E.W. Kolb, Cosmology of Biased Discrete Symmetry Breaking, Phys. Rev. D 39 (1989) 1558 [INSPIRE].
S.E. Larsson, S. Sarkar and P.L. White, Evading the cosmological domain wall problem, Phys. Rev. D 55 (1997) 5129 [hep-ph/9608319] [INSPIRE].
T. Hiramatsu, M. Kawasaki, K. Saikawa and T. Sekiguchi, Axion cosmology with long-lived domain walls, JCAP 01 (2013) 001 [arXiv:1207.3166] [INSPIRE].
D. Coulson, Z. Lalak and B.A. Ovrut, Biased domain walls, Phys. Rev. D 53 (1996) 4237 [INSPIRE].
M. Hindmarsh, Analytic scaling solutions for cosmic domain walls, Phys. Rev. Lett. 77 (1996) 4495 [hep-ph/9605332] [INSPIRE].
K.A. Beyer and S. Sarkar, Ruling out light axions: The writing is on the wall, SciPost Phys. 15 (2023) 003 [arXiv:2211.14635] [INSPIRE].
C.-F. Chang and Y. Cui, Dynamics of Long-lived Axion Domain Walls and Its Cosmological Implications, arXiv:2309.15920 [INSPIRE].
T. Hiramatsu, M. Kawasaki and K. Saikawa, Evolution of String-Wall Networks and Axionic Domain Wall Problem, JCAP 08 (2011) 030 [arXiv:1012.4558] [INSPIRE].
M. Kawasaki, K. Saikawa and T. Sekiguchi, Axion dark matter from topological defects, Phys. Rev. D 91 (2015) 065014 [arXiv:1412.0789] [INSPIRE].
G. Lazarides and Q. Shafi, Axion Models with No Domain Wall Problem, Phys. Lett. B 115 (1982) 21 [INSPIRE].
M. Gorghetto, E. Hardy and G. Villadoro, Axions from Strings: the Attractive Solution, JHEP 07 (2018) 151 [arXiv:1806.04677] [INSPIRE].
M. Buschmann et al., Dark matter from axion strings with adaptive mesh refinement, Nature Commun. 13 (2022) 1049 [arXiv:2108.05368] [INSPIRE].
M. Buschmann, J.W. Foster and B.R. Safdi, Early-Universe Simulations of the Cosmological Axion, Phys. Rev. Lett. 124 (2020) 161103 [arXiv:1906.00967] [INSPIRE].
T. Hiramatsu, M. Kawasaki, K. Saikawa and T. Sekiguchi, Production of dark matter axions from collapse of string-wall systems, Phys. Rev. D 85 (2012) 105020 [Erratum ibid. 86 (2012) 089902] [arXiv:1202.5851] [INSPIRE].
V.B. Klaer and G.D. Moore, The dark-matter axion mass, JCAP 11 (2017) 049 [arXiv:1708.07521] [INSPIRE].
M. Gorghetto, E. Hardy and G. Villadoro, More axions from strings, SciPost Phys. 10 (2021) 050 [arXiv:2007.04990] [INSPIRE].
M. Ardu et al., Axion quality from the (anti)symmetric of SU( ), JHEP 11 (2020) 090 [arXiv:2007.12663] [INSPIRE].
L. Di Luzio, E. Nardi and L. Ubaldi, Accidental Peccei-Quinn symmetry protected to arbitrary order, Phys. Rev. Lett. 119 (2017) 011801 [arXiv:1704.01122] [INSPIRE].
L.M. Krauss and F. Wilczek, Discrete Gauge Symmetry in Continuum Theories, Phys. Rev. Lett. 62 (1989) 1221 [INSPIRE].
B. Heidenreich et al., Non-invertible global symmetries and completeness of the spectrum, JHEP 09 (2021) 203 [arXiv:2104.07036] [INSPIRE].
J. Polchinski, Monopoles, duality, and string theory, Int. J. Mod. Phys. A 19S1 (2004) 145 [hep-th/0304042] [INSPIRE].
X. Niu, W. Xue and F. Yang, Gauged global strings, JHEP 02 (2024) 093 [arXiv:2311.07639] [INSPIRE].
D. Buttazzo et al., Scalar gauge dynamics and Dark Matter, JHEP 01 (2020) 130 [arXiv:1911.04502] [INSPIRE].
P. Laguna and R.A. Matzner, Peeling U(1) gauge cosmic strings, Phys. Rev. Lett. 62 (1989) 1948 [INSPIRE].
L.M.A. Bettencourt and T.W.B. Kibble, Nonintercommuting configurations in the collisions of type I U(1) cosmic strings, Phys. Lett. B 332 (1994) 297 [hep-ph/9405221] [INSPIRE].
L.M.A. Bettencourt, P. Laguna and R.A. Matzner, Nonintercommuting cosmic strings, Phys. Rev. Lett. 78 (1997) 2066 [hep-ph/9612350] [INSPIRE].
C.T. Hill, A.L. Kagan and L.M. Widrow, Are Cosmic Strings Frustrated?, Phys. Rev. D 38 (1988) 1100 [INSPIRE].
V.B. Klaer and G.D. Moore, How to simulate global cosmic strings with large string tension, JCAP 10 (2017) 043 [arXiv:1707.05566] [INSPIRE].
T. Hiramatsu, M. Ibe and M. Suzuki, New Type of String Solutions with Long Range Forces, JHEP 02 (2020) 058 [arXiv:1910.14321] [INSPIRE].
T. Hiramatsu, M. Ibe and M. Suzuki, Cosmic string in Abelian-Higgs model with enhanced symmetry — Implication to the axion domain-wall problem, JHEP 09 (2020) 054 [arXiv:2005.10421] [INSPIRE].
E.J. Copeland, T.W.B. Kibble and D.A. Steer, Collisions of strings with Y junctions, Phys. Rev. Lett. 97 (2006) 021602 [hep-th/0601153] [INSPIRE].
E.J. Copeland, T.W.B. Kibble and D.A. Steer, Constraints on string networks with junctions, Phys. Rev. D 75 (2007) 065024 [hep-th/0611243] [INSPIRE].
L. Di Luzio, F. Mescia and E. Nardi, Window for preferred axion models, Phys. Rev. D 96 (2017) 075003 [arXiv:1705.05370] [INSPIRE].
L. Di Luzio, F. Mescia and E. Nardi, Redefining the Axion Window, Phys. Rev. Lett. 118 (2017) 031801 [arXiv:1610.07593] [INSPIRE].
D. Tong, Line Operators in the Standard Model, JHEP 07 (2017) 104 [arXiv:1705.01853] [INSPIRE].
J. Davighi, B. Gripaios and N. Lohitsiri, Global anomalies in the Standard Model(s) and Beyond, JHEP 07 (2020) 232 [arXiv:1910.11277] [INSPIRE].
J. Kang, M.A. Luty and S. Nasri, The Relic abundance of long-lived heavy colored particles, JHEP 09 (2008) 086 [hep-ph/0611322] [INSPIRE].
C. Jacoby and S. Nussinov, The Relic Abundance of Massive Colored Particles after a Late Hadronic Annihilation Stage, arXiv:0712.2681 [INSPIRE].
B.A. Dobrescu, The Strong CP problem versus Planck scale physics, Phys. Rev. D 55 (1997) 5826 [hep-ph/9609221] [INSPIRE].
G. Veneziano, Large N bounds on, and compositeness limit of, gauge and gravitational interactions, JHEP 06 (2002) 051 [hep-th/0110129] [INSPIRE].
J.E. Kim, A composite invisible axion, Phys. Rev. D 31 (1985) 1733 [INSPIRE].
M. Redi and R. Sato, Composite Accidental Axions, JHEP 05 (2016) 104 [arXiv:1602.05427] [INSPIRE].
M.B. Gavela, M. Ibe, P. Quilez and T.T. Yanagida, Automatic Peccei-Quinn symmetry, Eur. Phys. J. C 79 (2019) 542 [arXiv:1812.08174] [INSPIRE].
S. Nakagawa, Y. Nakai, M. Yamada and Y. Zhang, Dynamics of superconformal axion: Quality and scalegenesis, Phys. Lett. B 849 (2024) 138447 [arXiv:2309.06964] [INSPIRE].
J.E. Kim and H.P. Nilles, The mu Problem and the Strong CP Problem, Phys. Lett. B 138 (1984) 150 [INSPIRE].
K.S. Babu, I. Gogoladze and K. Wang, Stabilizing the axion by discrete gauge symmetries, Phys. Lett. B 560 (2003) 214 [hep-ph/0212339] [INSPIRE].
K.S. Babu, I. Gogoladze and K. Wang, Natural R parity, μ-term, and fermion mass hierarchy from discrete gauge symmetries, Nucl. Phys. B 660 (2003) 322 [hep-ph/0212245] [INSPIRE].
H.M. Lee et al., A unique \( {\mathbb{Z}}_4^R \) symmetry for the MSSM, Phys. Lett. B 694 (2011) 491 [arXiv:1009.0905] [INSPIRE].
H.M. Lee et al., Discrete R symmetries for the MSSM and its singlet extensions, Nucl. Phys. B 850 (2011) 1 [arXiv:1102.3595] [INSPIRE].
H. Baer, V. Barger and D. Sengupta, Gravity safe, electroweak natural axionic solution to strong CP and SUSY μ problems, Phys. Lett. B 790 (2019) 58 [arXiv:1810.03713] [INSPIRE].
A. Hook, Solving the Hierarchy Problem Discretely, Phys. Rev. Lett. 120 (2018) 261802 [arXiv:1802.10093] [INSPIRE].
L. Di Luzio, B. Gavela, P. Quilez and A. Ringwald, An even lighter QCD axion, JHEP 05 (2021) 184 [arXiv:2102.00012] [INSPIRE].
M.B. Green and J.H. Schwarz, Anomaly Cancellation in Supersymmetric D=10 Gauge Theory and Superstring Theory, Phys. Lett. B 149 (1984) 117 [INSPIRE].
M. Dine, N. Seiberg and E. Witten, Fayet-Iliopoulos Terms in String Theory, Nucl. Phys. B 289 (1987) 589 [INSPIRE].
S.M. Barr, Harmless Axions in Superstring Theories, Phys. Lett. B 158 (1985) 397 [INSPIRE].
J.E. Kim, The Strong CP Problem in Orbifold Compactifications and an SU (3) × SU (2) × U (1)n Model, Phys. Lett. B 207 (1988) 434 [INSPIRE].
K. Choi, K.S. Jeong, K.-I. Okumura and M. Yamaguchi, Mixed Mediation of Supersymmetry Breaking with Anomalous U(1) Gauge Symmetry, JHEP 06 (2011) 049 [arXiv:1104.3274] [INSPIRE].
M. Cicoli et al., Explicit de Sitter Flux Vacua for Global String Models with Chiral Matter, JHEP 05 (2014) 001 [arXiv:1312.0014] [INSPIRE].
G. Honecker and W. Staessens, On axionic dark matter in Type IIA string theory, Fortsch. Phys. 62 (2014) 115 [arXiv:1312.4517] [INSPIRE].
K. Choi, K.S. Jeong and M.-S. Seo, String theoretic QCD axions in the light of PLANCK and BICEP2, JHEP 07 (2014) 092 [arXiv:1404.3880] [INSPIRE].
E.I. Buchbinder, A. Constantin and A. Lukas, Heterotic QCD axion, Phys. Rev. D 91 (2015) 046010 [arXiv:1412.8696] [INSPIRE].
H.-C. Cheng and D.E. Kaplan, Axions and a gauged Peccei-Quinn symmetry, hep-ph/0103346 [INSPIRE].
A.S. Chou et al., Snowmass Cosmic Frontier Report, in the proceedings of the Snowmass 2021, Seattle, U.S.A. (2022) [arXiv:2211.09978] [INSPIRE].
C. Csaki, M. Schmaltz and W. Skiba, Confinement in N=1 SUSY gauge theories and model building tools, Phys. Rev. D 55 (1997) 7840 [hep-th/9612207] [INSPIRE].
Acknowledgments
We have used the LATEX source of [107] to draw Young tableaux (and also found it a convenient reference for group theory factors). We would like to thank Nima Arkani-Hamed, Roberto Contino, Ben Heidenreich, Anson Hook, Joshua Lin, Maxim Perelstein, Alessandro Podo, Raman Sundrum, and Neal Weiner for helpful discussions. We thank an anonymous referee for useful comments, especially for asking us to clarify the logic of our Landau pole argument. QL is supported by the DOE grant DE-SC0013607, the NSF grant PHY-2210498 and PHY-2207584, and the Simons Foundation. MR is supported in part by the DOE Grant DE-SC0013607. ZS is supported by a fellowship from the MIT Department of Physics. This work was performed in part at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-2210452.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2312.07650
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Lu, Q., Reece, M. & Sun, Z. The quality/cosmology tension for a post-inflation QCD axion. J. High Energ. Phys. 2024, 227 (2024). https://doi.org/10.1007/JHEP07(2024)227
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2024)227