The swampland conjecture and the Higgs expectation value

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 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 longrange 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 finetuning 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. *

The Asymptotic dS Swampland Conjecture ‐ a Simplified Derivation and a Potential Loophole

“…Clearly, the realization of dS minima and of inflation in string theory is a difficult and important subject and such a revived attention is very desirable. An important point in our context is the suggestion of potential counter-examples to the original dS swampland conjecture in [15,24,27,30,32,39]. The refined version of the dS swampland conjecture advertised in [1], which is very close to that of [11], does not have these issues (see [8,9] for earlier suggestions for refinement).…”

Further Refining the de Sitter Swampland Conjecture

“…Those points are however not relevant to constrain the conjectures, so we do not include them in the following. It is interesting to note that the boundary curve for the new conjecture (1.5) always passes through the point (1,1), for any allowed 9 In this setting, one has D 6 and O 6 along four different sets of directions. As shown in [54], a sum of these sources contributions has to be negative to get a de Sitter solution, requiring as usual the presence of some O 6 , [55] but this does not need to hold for each of the four sets separately.…”

“…classical perturbative de Sitter string backgrounds (see [4] for a review, and [5] for some criticism) or particle physics scalar potentials (Higgs, QCD axion, neutral pion). [6][7][8][9]1 This situation has led to a call for a refined de Sitter conjecture, [11,12] which would only forbid de Sitter minima but allow maxima, i.e. unstable (tachyonic) de Sitter solutions: such a criterion has been formulated recently [13] (see also [12]) in the form of (1.3) detailed below.…”

On the weak gravity conjecture in string theory with broken supersymmetry

“…3 Fundamental constraints on the consistency of de Sitter vacua have been previously pointed out in [36,37]. After the appearance of possible counter examples [38][39][40][41][42][43] the original conjecture has been refined in [44], see also [45]. Other attempts of refinement were suggested in [46][47][48][49].…”