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(π0/fπ) = −1 implies c ≲ mathcal{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.
Highlights
JHEP11(2018)142 as well as on the parameter c defining the conjecture.1 it has been pointed out recently [6] that if the Standard Model (SM) sector is completely decoupled from the quintessence field φ, applying the dS swampland conjecture to the Higgs extremum results in c V (H = v)/V (H = 0) ∼ 10−55, which is smaller than the conjectured value c = O(1) by many orders of magnitude
In this paper we examined the implications of the pion or Higgs dS extrema for the dS swampland conjecture, while focusing on the possible bound on the parameter c
Applying the dS swampland conjecture to the pion extremum at cos(π0/fπ) = −1, we could derive a model-independent upper bound on c given in terms of the low energy quintessence couplings
Summary
We briefly discuss the possible couplings of the quintessence scalar field φ to the SM sector, as well as the observational constraints on the couplings. The field φ corresponds to the fluctuation around φ0, and the ellipsis stands for additional couplings which are not relevant for our subsequent discussion As they are even weaker than the gravitational coupling, the quintessence couplings are constrained mostly by the macroscopic observations such as the violation of the equivalence principle in non-relativistic limit, the deviation from the general relativity in relativistic limit, or the variation of the fundamental constants, e.g. the fine structure constant [35]. Those constraints apply for the low energy effective couplings of φ defined at lower energy scale μeff , which may be parametrized as.
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