The swampland conjecture and the Higgs expectation value
  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 with 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.
