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Journal of High Energy Physics

, 2018:23 | Cite as

The swampland conjecture and the Higgs expectation value

  • Koichi Hamaguchi
  • Masahiro IbeEmail author
  • Takeo Moroi
Open Access
Regular Article - Theoretical Physics

Abstract

The recently proposed de Sitter swampland conjecture excludes local extrema of a scalar potential with a positive energy density in a low energy effective theory. Under the conjecture, the observed dark energy cannot be explained by the cosmological constant. The local maximum of the Higgs potential at the symmetric point also contradicts the conjecture. In order to make the Standard Model consistent with the conjecture, it has been proposed to introduce a quintessence field, Q, which couples to the cosmological constant and the local maximum of the Higgs potential. In this paper, we show that such a modified Higgs potential generically results in a Q-dependent Higgs vacuum expectation value (VEV). The Q-dependence of the Higgs VEV induces a long-range force, which is severely excluded by the tests of the equivalence principle. Besides, as the quintessence field is in motion, the Higgs VEV shows a time-dependence, which is also severely constrained by the measurements of the time-dependence of the proton-to-electron mass ratio. Those constraints require an additional fine-tuning which is justified neither by the swampland conjecture nor the anthropic principle. We further show that, even if such an unjustified fine-tuning condition is imposed at the tree level, radiative corrections upset it. Consequently, we argue that most of the habitable vacua in the string landscape are in tension with the phenomenological constraints.

Keywords

Effective Field Theories Renormalization Group Renormalization Regularization and Renormalons 

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]
    C. Vafa, The string landscape and the swampland, hep-th/0509212 [INSPIRE].
  2. [2]
    H. Ooguri and C. Vafa, On the geometry of the string landscape and the swampland, Nucl. Phys. B 766 (2007) 21 [hep-th/0605264] [INSPIRE].
  3. [3]
    H. Ooguri and C. Vafa, Non-supersymmetric AdS and the swampland, Adv. Theor. Math. Phys. 21 (2017) 1787 [arXiv:1610.01533] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, De Sitter space and the swampland, arXiv:1806.08362 [INSPIRE].
  5. [5]
    S. Vagnozzi et al., Constraints on the sum of the neutrino masses in dynamical dark energy models with w(z) ≥ −1 are tighter than those obtained in ΛCDM, Phys. Rev. D 98 (2018) 083501 [arXiv:1801.08553] [INSPIRE].
  6. [6]
    P. Agrawal, G. Obied, P.J. Steinhardt and C. Vafa, On the cosmological implications of the string swampland, Phys. Lett. B 784 (2018) 271 [arXiv:1806.09718] [INSPIRE].
  7. [7]
    D. Andriot, On the de Sitter swampland criterion, Phys. Lett. B 785 (2018) 570 [arXiv:1806.10999] [INSPIRE].
  8. [8]
    A. Achúcarro and G.A. Palma, The string swampland constraints require multi-field inflation, arXiv:1807.04390 [INSPIRE].
  9. [9]
    S.K. Garg and C. Krishnan, Bounds on slow roll and the de Sitter swampland, arXiv:1807.05193 [INSPIRE].
  10. [10]
    J.-L. Lehners, Small-field and scale-free: inflation and Ekpyrosis at their extremes, JCAP 11 (2018) 001 [arXiv:1807.05240] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    A. Kehagias and A. Riotto, A note on inflation and the swampland, arXiv:1807.05445 [INSPIRE].
  12. [12]
    M. Dias, J. Frazer, A. Retolaza and A. Westphal, Primordial gravitational waves and the swampland, arXiv:1807.06579 [INSPIRE].
  13. [13]
    F. Denef, A. Hebecker and T. Wrase, De Sitter swampland conjecture and the Higgs potential, Phys. Rev. D 98 (2018) 086004 [arXiv:1807.06581] [INSPIRE].
  14. [14]
    E. Ó. Colgáin, M.H. P.M. Van Putten and H. Yavartanoo, Observational consequences of H 0 tension in de Sitter Swampland, arXiv:1807.07451 [INSPIRE].
  15. [15]
    R. Brandenberger, L.L. Graef, G. Marozzi and G.P. Vacca, Back-reaction of super-hubble cosmological perturbations beyond perturbation theory, arXiv:1807.07494 [INSPIRE].
  16. [16]
    S. Paban and R. Rosati, Inflation in multi-field modified DBM potentials, JCAP 09 (2018) 042 [arXiv:1807.07654] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    A. Ghalee, Condensation of a scalar field non-minimally coupled to gravity in a cosmological context, arXiv:1807.08620 [INSPIRE].
  18. [18]
    H. Matsui and F. Takahashi, Eternal inflation and swampland conjectures, arXiv:1807.11938 [INSPIRE].
  19. [19]
    I. Ben-Dayan, Draining the swampland, arXiv:1808.01615 [INSPIRE].
  20. [20]
    C.-I. Chiang and H. Murayama, Building supergravity quintessence model, arXiv:1808.02279 [INSPIRE].
  21. [21]
    L. Heisenberg, M. Bartelmann, R. Brandenberger and A. Refregier, Dark energy in the swampland, arXiv:1808.02877 [INSPIRE].
  22. [22]
    C. Damian and O. Loaiza-Brito, Two-field axion inflation and the swampland constraint in the flux-scaling scenario, arXiv:1808.03397 [INSPIRE].
  23. [23]
    W.H. Kinney, S. Vagnozzi and L. Visinelli, The zoo plot meets the swampland: mutual (in)consistency of single-field inflation, string conjectures and cosmological data, arXiv:1808.06424 [INSPIRE].
  24. [24]
    Y. Akrami, R. Kallosh, A. Linde and V. Vardanyan, The landscape, the swampland and the era of precision cosmology, arXiv:1808.09440 [INSPIRE].
  25. [25]
    L. Heisenberg, M. Bartelmann, R. Brandenberger and A. Refregier, Dark energy in the swampland II, arXiv:1809.00154 [INSPIRE].
  26. [26]
    H. Murayama, M. Yamazaki and T.T. Yanagida, Do we live in the swampland?, arXiv:1809.00478 [INSPIRE].
  27. [27]
    M.C.D. Marsh, The swampland, quintessence and the vacuum energy, arXiv:1809.00726 [INSPIRE].
  28. [28]
    S. Brahma and M. Wali Hossain, Avoiding the string swampland in single-field inflation: excited initial states, arXiv:1809.01277 [INSPIRE].
  29. [29]
    K. Choi, D. Chway and C.S. Shin, The dS swampland conjecture with the electroweak symmetry and QCD chiral symmetry breaking, arXiv:1809.01475 [INSPIRE].
  30. [30]
    S. Das, A note on single-field inflation and the swampland criteria, arXiv:1809.03962 [INSPIRE].
  31. [31]
    U. Danielsson, The quantum swampland, arXiv:1809.04512 [INSPIRE].
  32. [32]
    R.H. Brandenberger, Beyond standard inflationary cosmology, arXiv:1809.04926 [INSPIRE].
  33. [33]
    C. Han, S. Pi and M. Sasaki, Quintessence saves Higgs instability, arXiv:1809.05507 [INSPIRE].
  34. [34]
    R. Brandenberger, R.R. Cuzinatto, J. Fröhlich and R. Namba, New scalar field quartessence, arXiv:1809.07409 [INSPIRE].
  35. [35]
    H. Matsui, F. Takahashi and M. Yamada, Isocurvature perturbations of dark energy and dark matter from the swampland conjecture, arXiv:1809.07286 [INSPIRE].
  36. [36]
    M. Cicoli et al., De Sitter vs. quintessence in string theory, Fortsch. Phys. (2018) 1800079 [arXiv:1808.08967] [INSPIRE].
  37. [37]
    B. Ratra and P.J.E. Peebles, Cosmological consequences of a rolling homogeneous scalar field, Phys. Rev. D 37 (1988) 3406 [INSPIRE].
  38. [38]
    C. Wetterich, Cosmology and the fate of dilatation symmetry, Nucl. Phys. B 302 (1988) 668 [arXiv:1711.03844] [INSPIRE].
  39. [39]
    S. Tsujikawa, Quintessence: a review, Class. Quant. Grav. 30 (2013) 214003 [arXiv:1304.1961] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    T.A. Wagner, S. Schlamminger, J.H. Gundlach and E.G. Adelberger, Torsion-balance tests of the weak equivalence principle, Class. Quant. Grav. 29 (2012) 184002 [arXiv:1207.2442] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    C.J. A.P. Martins, The status of varying constants: a review of the physics, searches and implications, arXiv:1709.02923 [INSPIRE].
  42. [42]
    Planck collaboration, N. Aghanim et al., Planck 2018 results. VI. Cosmological parameters, arXiv:1807.06209 [INSPIRE].
  43. [43]
    R. Bousso and J. Polchinski, Quantization of four form fluxes and dynamical neutralization of the cosmological constant, JHEP 06 (2000) 006 [hep-th/0004134] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    L. Susskind, The anthropic landscape of string theory, hep-th/0302219 [INSPIRE].
  45. [45]
    M. Tegmark, A. Aguirre, M. Rees and F. Wilczek, Dimensionless constants, cosmology and other dark matters, Phys. Rev. D 73 (2006) 023505 [astro-ph/0511774] [INSPIRE].
  46. [46]
    M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Remarks on Higgs boson interactions with nucleons, Phys. Lett. B 78 (1978) 443.Google Scholar
  47. [47]
    M. Hoferichter, P. Klos, J. Menéndez and A. Schwenk, Improved limits for Higgs-portal dark matter from LHC searches, Phys. Rev. Lett. 119 (2017) 181803 [arXiv:1708.02245] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    A. Crivellin, M. Hoferichter and M. Procura, Accurate evaluation of hadronic uncertainties in spin-independent WIMP-nucleon scattering: Disentangling two- and three-flavor effects, Phys. Rev. D 89 (2014) 054021 [arXiv:1312.4951] [INSPIRE].
  49. [49]
    D. Wang, The multi-feature universe: large parameter space cosmology and the swampland, arXiv:1809.04854 [INSPIRE].
  50. [50]
    L.J. Hall, D. Pinner and J.T. Ruderman, The weak scale from BBN, JHEP 12 (2014) 134 [arXiv:1409.0551] [INSPIRE].
  51. [51]
    R. Harnik, G.D. Kribs and G. Perez, A universe without weak interactions, Phys. Rev. D 74 (2006) 035006 [hep-ph/0604027] [INSPIRE].
  52. [52]
    B.A. Campbell and K.A. Olive, Nucleosynthesis and the time dependence of fundamental couplings, Phys. Lett. B 345 (1995) 429 [hep-ph/9411272] [INSPIRE].
  53. [53]
    E.J. Weinberg and A.-q. Wu, Understanding complex perturbative effective potentials, Phys. Rev. D 36 (1987) 2474 [INSPIRE].
  54. [54]
    C. Ford, I. Jack and D.R.T. Jones, The standard model effective potential at two loops, Nucl. Phys. B 387 (1992) 373 [Erratum ibid. B 504 (1997) 551] [hep-ph/0111190] [INSPIRE].
  55. [55]
    S.P. Martin, Three-loop standard model effective potential at leading order in strong and top Yukawa couplings, Phys. Rev. D 89 (2014) 013003 [arXiv:1310.7553] [INSPIRE].
  56. [56]
    G. Degrassi et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    Particle Data Group collaboration, M. Tanabashi et al., Review of particle physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
  58. [58]
    S.P. Martin and D.G. Robertson, Higgs boson mass in the standard model at two-loop order and beyond, Phys. Rev. D 90 (2014) 073010 [arXiv:1407.4336] [INSPIRE].
  59. [59]
    S.P. Martin and D.G. Robertson, TSIL: a program for the calculation of two-loop self-energy integrals, Comput. Phys. Commun. 174 (2006) 133 [hep-ph/0501132] [INSPIRE].
  60. [60]
    H. Ooguri, E. Palti, G. Shiu and C. Vafa, Distance and de Sitter conjectures on the swampland, arXiv:1810.05506 [INSPIRE].
  61. [61]
    E.J. Copeland, A.R. Liddle and D. Wands, Exponential potentials and cosmological scaling solutions, Phys. Rev. D 57 (1998) 4686 [gr-qc/9711068] [INSPIRE].
  62. [62]
    P.G. Ferreira and M. Joyce, Cosmology with a primordial scaling field, Phys. Rev. D 58 (1998) 023503 [astro-ph/9711102] [INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Koichi Hamaguchi
    • 1
    • 2
  • Masahiro Ibe
    • 2
    • 3
    Email author
  • Takeo Moroi
    • 1
    • 2
  1. 1.Department of Physics, Faculty of ScienceThe University of TokyoTokyoJapan
  2. 2.Kavli IPMU (WPI), UTIAS, The University of TokyoKashiwaJapan
  3. 3.ICRR, The University of TokyoKashiwaJapan

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