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Relaxing the cosmological moduli problem by low-scale inflation

  • Shu-Yu Ho
  • Fuminobu Takahashi
  • Wen YinEmail author
Open Access
Regular Article - Theoretical Physics
  • 34 Downloads

Abstract

We show that the cosmological abundance of string axions is much smaller than naive estimates if the Hubble scale of inflation, Hinf , is sufficiently low (but can still be much higher than the axion masses) and if the inflation lasts sufficiently long. The reason is that the initial misalignment angles of the string axions follow the Bunch-Davies distribution peaked at the potential minima. As a result, the cosmological moduli problem induced by the string axions can be significantly relaxed by low-scale inflation, and astrophysical and cosmological bounds are satisfied over a wide range of the mass without any fine-tuning of the initial misalignment angles. Specifically, the axion with its decay constant fϕ = 1016 GeV satisfies the bounds over 10−18 eV ≲ mϕ ≲ 10 TeV for Hinf ≲ 10 keV-106 GeV. We also discuss cases with multiple axions and the QCD axion.

Keywords

Cosmology of Theories beyond the SM Beyond Standard Model Compactification and String Models Supersymmetric Standard Model 

Notes

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.

References

  1. [1]
    J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string, Cambridge University Press (2007) [INSPIRE].
  2. [2]
    G.D. Coughlan, W. Fischler, E.W. Kolb, S. Raby and G.G. Ross, Cosmological Problems for the Polonyi Potential, Phys. Lett. 131B (1983) 59 [INSPIRE].
  3. [3]
    B. de Carlos, J.A. Casas, F. Quevedo and E. Roulet, Model independent properties and cosmological implications of the dilaton and moduli sectors of 4-D strings, Phys. Lett. B 318 (1993) 447 [hep-ph/9308325] [INSPIRE].
  4. [4]
    M. Graña, Flux compactifications in string theory: A Comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    R. Blumenhagen, B. Körs, D. Lüst and S. Stieberger, Four-dimensional String Compactifications with D-branes, Orientifolds and Fluxes, Phys. Rept. 445 (2007) 1 [hep-th/0610327] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    L. Görlich, S. Kachru, P.K. Tripathy and S.P. Trivedi, Gaugino condensation and nonperturbative superpotentials in flux compactifications, JHEP 12 (2004) 074 [hep-th/0407130] [INSPIRE].MathSciNetGoogle Scholar
  7. [7]
    S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
  8. [8]
    P. Svrček and E. Witten, Axions In String Theory, JHEP 06 (2006) 051 [hep-th/0605206] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    J.P. Conlon, The QCD axion and moduli stabilisation, JHEP 05 (2006) 078 [hep-th/0602233] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    K. Choi and K.S. Jeong, String theoretic QCD axion with stabilized saxion and the pattern of supersymmetry breaking, JHEP 01 (2007) 103 [hep-th/0611279] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper and J. March-Russell, String Axiverse, Phys. Rev. D 81 (2010) 123530 [arXiv:0905.4720] [INSPIRE].
  12. [12]
    B.S. Acharya, K. Bobkov and P. Kumar, An M-theory Solution to the Strong CP Problem and Constraints on the Axiverse, JHEP 11 (2010) 105 [arXiv:1004.5138] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  13. [13]
    T. Higaki and T. Kobayashi, Note on moduli stabilization, supersymmetry breaking and axiverse, Phys. Rev. D 84 (2011) 045021 [arXiv:1106.1293] [INSPIRE].
  14. [14]
    M. Cicoli, M. Goodsell and A. Ringwald, The type IIB string axiverse and its low-energy phenomenology, JHEP 10 (2012) 146 [arXiv:1206.0819] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    M. Cicoli, S. de Alwis and A. Westphal, Heterotic Moduli Stabilisation, JHEP 10 (2013) 199 [arXiv:1304.1809] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    L. Visinelli and S. Vagnozzi, Cosmological window onto the string axiverse and the supersymmetry breaking scale, Phys. Rev. D 99 (2019) 063517 [arXiv:1809.06382] [INSPIRE].
  17. [17]
    M. Kawasaki, K. Kohri and T. Moroi, Big-Bang nucleosynthesis and hadronic decay of long-lived massive particles, Phys. Rev. D 71 (2005) 083502 [astro-ph/0408426] [INSPIRE].
  18. [18]
    M. Kawasaki, K. Kohri, T. Moroi and Y. Takaesu, Revisiting Big-Bang Nucleosynthesis Constraints on Long-Lived Decaying Particles, Phys. Rev. D 97 (2018) 023502 [arXiv:1709.01211] [INSPIRE].
  19. [19]
    M. Kawasaki and T. Yanagida, Constraint on cosmic density of the string moduli field in gauge mediated supersymmetry breaking theories, Phys. Lett. B 399 (1997) 45 [hep-ph/9701346] [INSPIRE].
  20. [20]
    T. Asaka, J. Hashiba, M. Kawasaki and T. Yanagida, Cosmological moduli problem in gauge mediated supersymmetry breaking theories, Phys. Rev. D 58 (1998) 083509 [hep-ph/9711501] [INSPIRE].
  21. [21]
    T. Asaka and M. Kawasaki, Cosmological moduli problem and thermal inflation models, Phys. Rev. D 60 (1999) 123509 [hep-ph/9905467] [INSPIRE].
  22. [22]
    M. Endo, K. Hamaguchi and F. Takahashi, Moduli-induced gravitino problem, Phys. Rev. Lett. 96 (2006) 211301 [hep-ph/0602061] [INSPIRE].
  23. [23]
    S. Nakamura and M. Yamaguchi, Gravitino production from heavy moduli decay and cosmological moduli problem revived, Phys. Lett. B 638 (2006) 389 [hep-ph/0602081 [INSPIRE].
  24. [24]
    M. Dine, R. Kitano, A. Morisse and Y. Shirman, Moduli decays and gravitinos, Phys. Rev. D 73 (2006) 123518 [hep-ph/0604140] [INSPIRE].
  25. [25]
    M. Endo, K. Hamaguchi and F. Takahashi, Moduli/Inflaton Mixing with Supersymmetry Breaking Field, Phys. Rev. D 74 (2006) 023531 [hep-ph/0605091] [INSPIRE].
  26. [26]
    M. Cicoli, J.P. Conlon and F. Quevedo, Dark radiation in LARGE volume models, Phys. Rev. D 87 (2013) 043520 [arXiv:1208.3562] [INSPIRE].
  27. [27]
    T. Higaki and F. Takahashi, Dark Radiation and Dark Matter in Large Volume Compactifications, JHEP 11 (2012) 125 [arXiv:1208.3563] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    T. Higaki, K. Nakayama and F. Takahashi, Moduli-Induced Axion Problem, JHEP 07 (2013) 005 [arXiv:1304.7987] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    K. Yamamoto, Phase Transition Associated With Intermediate Gauge Symmetry Breaking in Superstring Models, Phys. Lett. 168B (1986) 341 [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    D.H. Lyth and E.D. Stewart, Thermal inflation and the moduli problem, Phys. Rev. D 53 (1996) 1784 [hep-ph/9510204] [INSPIRE].
  31. [31]
    I. Affleck and M. Dine, A New Mechanism for Baryogenesis, Nucl. Phys. B 249 (1985) 361 [INSPIRE].
  32. [32]
    M. Dine, L. Randall and S.D. Thomas, Baryogenesis from flat directions of the supersymmetric standard model, Nucl. Phys. B 458 (1996) 291 [hep-ph/9507453] [INSPIRE].
  33. [33]
    S. Kasuya, M. Kawasaki and F. Takahashi, On the moduli problem and baryogenesis in gauge mediated SUSY breaking models, Phys. Rev. D 65 (2002) 063509 [hep-ph/0108171] [INSPIRE].
  34. [34]
    E.D. Stewart, M. Kawasaki and T. Yanagida, Affleck-Dine baryogenesis after thermal inflation, Phys. Rev. D 54 (1996) 6032 [hep-ph/9603324] [INSPIRE].
  35. [35]
    L. Randall and S.D. Thomas, Solving the cosmological moduli problem with weak scale inflation, Nucl. Phys. B 449 (1995) 229 [hep-ph/9407248] [INSPIRE].
  36. [36]
    R. Daido, F. Takahashi and W. Yin, The ALP miracle: unified inflaton and dark matter, JCAP 05 (2017) 044 [arXiv:1702.03284] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    R. Daido, F. Takahashi and W. Yin, The ALP miracle revisited, JHEP 02 (2018) 104 [arXiv:1710.11107] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    F. Takahashi and W. Yin, ALP inflation and Big Bang on Earth, arXiv:1903.00462 [INSPIRE].
  39. [39]
    A.D. Linde, Relaxing the cosmological moduli problem, Phys. Rev. D 53 (1996) R4129 [hep-th/9601083] [INSPIRE].
  40. [40]
    K. Nakayama, F. Takahashi and T.T. Yanagida, On the Adiabatic Solution to the Polonyi/Moduli Problem, Phys. Rev. D 84 (2011) 123523 [arXiv:1109.2073] [INSPIRE].
  41. [41]
    K. Nakayama, F. Takahashi and T.T. Yanagida, Cosmological Moduli Problem in Low Cutoff Theory, Phys. Rev. D 86 (2012) 043507 [arXiv:1112.0418] [INSPIRE].
  42. [42]
    P.J. Steinhardt, Natural inflation in The Very Early Universe, Proceedings of the Nuffield Workshop, G.W. Gibbons, S.W. Hawking and S.T.C. Siklos eds., Cambridge, 21 June-9 July 1982, Cambridge University Press (1985) [INSPIRE].
  43. [43]
    A. Vilenkin, The Birth of Inflationary Universes, Phys. Rev. D 27 (1983) 2848 [INSPIRE].
  44. [44]
    A.D. Linde, Eternal chaotic inflation, Mod. Phys. Lett. A 1 (1986) 81 [INSPIRE].
  45. [45]
    A.D. Linde, Eternally Existing Selfreproducing Chaotic Inflationary Universe, Phys. Lett. B 175 (1986) 395 [INSPIRE].
  46. [46]
    A.S. Goncharov, A.D. Linde and V.F. Mukhanov, The Global Structure of the Inflationary Universe, Int. J. Mod. Phys. A 2 (1987) 561 [INSPIRE].
  47. [47]
    A.H. Guth, Eternal inflation and its implications, J. Phys. A 40 (2007) 6811 [hep-th/0702178] [INSPIRE].
  48. [48]
    A.H. Guth, Inflation and eternal inflation, Phys. Rept. 333 (2000) 555 [astro-ph/0002156] [INSPIRE].
  49. [49]
    A. Vilenkin, A Measure of the multiverse, J. Phys. A 40 (2007) 6777 [hep-th/0609193] [INSPIRE].
  50. [50]
    S. Winitzki, Predictions in eternal inflation, Lect. Notes Phys. 738 (2008) 157 [gr-qc/0612164] [INSPIRE].
  51. [51]
    A.D. Linde, Inflationary Cosmology, Lect. Notes Phys. 738 (2008) 1 [arXiv:0705.0164] [INSPIRE].
  52. [52]
    T.S. Bunch and P.C.W. Davies, Quantum Field Theory in de Sitter Space: Renormalization by Point Splitting, Proc. Roy. Soc. Lond. A 360 (1978) 117 [INSPIRE].
  53. [53]
    P.W. Graham and A. Scherlis, Stochastic axion scenario, Phys. Rev. D 98 (2018) 035017 [arXiv:1805.07362] [INSPIRE].
  54. [54]
    F. Takahashi, W. Yin and A.H. Guth, QCD axion window and low-scale inflation, Phys. Rev. D 98 (2018) 015042 [arXiv:1805.08763] [INSPIRE].
  55. [55]
    R. Essig, E. Kuflik, S.D. McDermott, T. Volansky and K.M. Zurek, Constraining Light Dark Matter with Diffuse X-Ray and Gamma-Ray Observations, JHEP 11 (2013) 193 [arXiv:1309.4091] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    J.F. Navarro, C.S. Frenk and S.D.M. White, The Structure of cold dark matter halos, Astrophys. J. 462 (1996) 563 [astro-ph/9508025] [INSPIRE].
  57. [57]
    J.F. Navarro, C.S. Frenk and S.D.M. White, A Universal density profile from hierarchical clustering, Astrophys. J. 490 (1997) 493 [astro-ph/9611107] [INSPIRE].
  58. [58]
    S. Dimopoulos and L.J. Hall, Inflation and Invisible Axions, Phys. Rev. Lett. 60 (1988) 1899 [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    G.W. Gibbons and S.W. Hawking, Cosmological Event Horizons, Thermodynamics and Particle Creation, Phys. Rev. D 15 (1977) 2738 [INSPIRE].
  60. [60]
    T. Higaki and F. Takahashi, Natural and Multi-Natural Inflation in Axion Landscape, JHEP 07 (2014) 074 [arXiv:1404.6923] [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    T. Higaki and F. Takahashi, Axion Landscape and Natural Inflation, Phys. Lett. B 744 (2015) 153 [arXiv:1409.8409] [INSPIRE].
  62. [62]
    G. Wang and T. Battefeld, Vacuum Selection on Axionic Landscapes, JCAP 04 (2016) 025 [arXiv:1512.04224] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  63. [63]
    A. Masoumi and A. Vilenkin, Vacuum statistics and stability in axionic landscapes, JCAP 03 (2016) 054 [arXiv:1601.01662] [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    R. Daido, T. Kobayashi and F. Takahashi, Dark Matter in Axion Landscape, Phys. Lett. B 765 (2017) 293 [arXiv:1608.04092] [INSPIRE].
  65. [65]
    T. Kugo and T. Yanagida, Unification of Families Based on a Coset Space E 7 /SU(5) × SU(3) × U(1), Phys. Lett. 134B (1984) 313 [INSPIRE].
  66. [66]
    T. Yanagida and Y. Yasui, Supersymmetric nonlinear σ-models based on exceptional groups, Nucl. Phys. B 269 (1986) 575 [INSPIRE].
  67. [67]
    Z. Komargodski and N. Seiberg, Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity, JHEP 07 (2010) 017 [arXiv:1002.2228] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  68. [68]
    T. Kugo and T.T. Yanagida, Coupling Supersymmetric Nonlinear σ-models to Supergravity, Prog. Theor. Phys. 124 (2010) 555 [arXiv:1003.5985] [INSPIRE].
  69. [69]
    T.T. Yanagida, W. Yin and N. Yokozaki, Nambu-Goldstone Boson Hypothesis for Squarks and Sleptons in Pure Gravity Mediation, JHEP 09 (2016) 086 [arXiv:1608.06618] [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    M. Yamaguchi and W. Yin, A novel approach to finely tuned supersymmetric standard models: The case of the non-universal Higgs mass model, PTEP 2018 (2018) 023B06 [arXiv:1606.04953] [INSPIRE].
  71. [71]
    W. Yin and N. Yokozaki, Splitting mass spectra and muon g − 2 in Higgs-anomaly mediation, Phys. Lett. B 762 (2016) 72 [arXiv:1607.05705] [INSPIRE].
  72. [72]
    T.T. Yanagida, W. Yin and N. Yokozaki, Flavor-Safe Light Squarks in Higgs-Anomaly Mediation, JHEP 04 (2018) 012 [arXiv:1801.05785] [INSPIRE].CrossRefzbMATHGoogle Scholar
  73. [73]
    M. Fukugita and T. Yanagida, Baryogenesis Without Grand Unification, Phys. Lett. B 174 (1986) 45 [INSPIRE].
  74. [74]
    W. Buchmüller, R.D. Peccei and T. Yanagida, Leptogenesis as the origin of matter, Ann. Rev. Nucl. Part. Sci. 55 (2005) 311 [hep-ph/0502169] [INSPIRE].
  75. [75]
    S. Davidson, E. Nardi and Y. Nir, Leptogenesis, Phys. Rept. 466 (2008) 105 [arXiv:0802.2962] [INSPIRE].
  76. [76]
    Y. Hamada and R. Kitano, Primordial Lepton Oscillations and Baryogenesis, JHEP 11 (2016) 010 [arXiv:1609.05028] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  77. [77]
    Y. Hamada, R. Kitano and W. Yin, Leptogenesis via Neutrino Oscillation Magic, JHEP 10 (2018) 178 [arXiv:1807.06582] [INSPIRE].ADSCrossRefGoogle Scholar
  78. [78]
    J. Preskill, S.P. Trivedi, F. Wilczek and M.B. Wise, Cosmology and broken discrete symmetry, Nucl. Phys. B 363 (1991) 207 [INSPIRE].
  79. [79]
    M. Dine and W. Fischler, The Not So Harmless Axion, Phys. Lett. B 120 (1983) 137 [INSPIRE].ADSCrossRefGoogle Scholar
  80. [80]
    L.F. Abbott and P. Sikivie, A Cosmological Bound on the Invisible Axion, Phys. Lett. B 120 (1983) 133 [INSPIRE].
  81. [81]
    G.R. Dvali, Removing the cosmological bound on the axion scale, hep-ph/9505253 [INSPIRE].
  82. [82]
    T. Banks and M. Dine, The Cosmology of string theoretic axions, Nucl. Phys. B 505 (1997) 445 [hep-th/9608197] [INSPIRE].
  83. [83]
    K.S. Jeong and F. Takahashi, Suppressing Isocurvature Perturbations of QCD Axion Dark Matter, Phys. Lett. B 727 (2013) 448 [arXiv:1304.8131] [INSPIRE].
  84. [84]
    R.T. Co, E. Gonzalez and K. Harigaya, Axion Misalignment Driven to the Bottom, arXiv:1812.11186 [INSPIRE].
  85. [85]
    K. Choi, H.B. Kim and J.E. Kim, Axion cosmology with a stronger QCD in the early universe, Nucl. Phys. B 490 (1997) 349 [hep-ph/9606372] [INSPIRE].
  86. [86]
    Y. Hamada, K.-y. Oda and F. Takahashi, Topological Higgs inflation: Origin of Standard Model criticality, Phys. Rev. D 90 (2014) 097301 [arXiv:1408.5556] [INSPIRE].
  87. [87]
    C.D. Froggatt and H.B. Nielsen, Standard model criticality prediction: Top mass 173 ± 5 GeV and Higgs mass 135 ± 9 GeV, Phys. Lett. B 368 (1996) 96 [hep-ph/9511371] [INSPIRE].

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of PhysicsTohoku UniversitySendaiJapan
  2. 2.Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU)UTIAS, WPI, The University of TokyoKashiwaJapan
  3. 3.Department of PhysicsKorea Advanced Institute of Science and TechnologyDaejeonKorea

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