The dS swampland conjecture with the electroweak symmetry and QCD chiral symmetry breaking

Abstract

The dS swampland conjecture |∇V |/V ≥ c, where c is presumed to be a positive constant of order unity, implies that the dark energy density of our Universe can not be a cosmological constant, but mostly the potential energy of an evolving quintessence scalar field. As the dark energy includes the effects of the electroweak symmetry breaking and the QCD chiral symmetry breaking, if the dS swampland conjecture is applicable for the low energy quintessence potential, it can be applied for the Higgs and pion potential also. On the other hand, the Higgs and pion potential has the well-known dS extrema, and applying the dS swampland conjecture to those dS extrema may provide stringent constraints on the viable quintessence, as well as on the conjecture itself. We examine this issue and find that the pion dS extremum at cos(π 0 /f π ) = −1 implies c O(10 −2 − 10 −5 ) for arbitrary form of the quintessence potential and couplings, where the weaker bound (10 −2 ) is available only for a specific type of quintessence whose couplings respect the equivalence principle, while the stronger bound (10 −5 ) applies for generic quintessence violating the equivalence principle. We also discuss the possibility to relax this bound with an additional scalar field, e.g. a light modulus which has a runaway behavior at the pion dS extremum. We argue that such possibility is severely constrained by a variety of observational constraints which do not leave a room to significantly relax the bound. We make a similar analysis for the Higgs dS extremum at H = 0, which results in a weaker bound on c. * Electronic address: kchoi@ibs.re.kr † Electronic address:

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).…”

The Swampland: Introduction and Review

“…But we see that the Refined de Sitter conjecture is certainly satisfied. Similarly, it was argued that the QCD axion and the QCD phase transition would be associated to violations of the original conjecture . It was shown in [] that the refined de Sitter conjecture avoids these counter examples.…”

Further Refining the de Sitter Swampland Conjecture

“…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.…”

“…We still use here the same framework, based on [37]. 8 Our various data points, coming from [5], correspond to different group manifolds and underlying algebras, as well as different orbifolds, which in turn select different flux components. For each of these possibilities, our numerical approach minimizes V , sometimes reaching a numerical 0, thus obtaining a de Sitter solution.…”