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


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.


Effective Field Theories Renormalization Group Renormalization Regularization and Renormalons 


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.


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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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