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

Kiwoon Choi, Dongjin Chway, Chang Sub Shin

TL;DR

The paper probes whether the de Sitter swampland conjecture with a nominally order-one constant $c$ can coexist with low-energy physics that includes electroweak and QCD effects by analyzing the pion and Higgs dS extrema within a general quintessence framework. It derives explicit bounds on $c$ in terms of the light-quark and gluon couplings $d_q$ and $d_g$, distinguishing between metrical (equivalence-principle–respecting) and generic EP-violating quintessence; the pion extremum yields the strongest constraint. Specifically, from the pion extremum one obtains $c \lesssim \max\left[d_{\tilde q}+3 d_g, {\cal O}(10^{-43})\right]$, which under current EP bounds translates to $c \lesssim 2\times 10^{-5}$ for EP-violating quintessence and $c \lesssim 1.4\times 10^{-2}$ for metrical quintessence, while the Higgs extremum gives $c \lesssim 4.4\times 10^{-2}$. The possibility of relaxing these bounds via a light modulus or tadpole is shown to be severely constrained by astrophysical and cosmological data, leaving little room to accommodate $c={\cal O}(1)$ and suggesting a need for refinements of the conjecture.

Abstract

The dS swampland conjecture $|\nabla V|/V \geq c$, 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 $c\lesssim {\cal O}(10^{-2}-10^{-5})$ 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 $c$.

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

TL;DR

The paper probes whether the de Sitter swampland conjecture with a nominally order-one constant can coexist with low-energy physics that includes electroweak and QCD effects by analyzing the pion and Higgs dS extrema within a general quintessence framework. It derives explicit bounds on in terms of the light-quark and gluon couplings and , distinguishing between metrical (equivalence-principle–respecting) and generic EP-violating quintessence; the pion extremum yields the strongest constraint. Specifically, from the pion extremum one obtains , which under current EP bounds translates to for EP-violating quintessence and for metrical quintessence, while the Higgs extremum gives . The possibility of relaxing these bounds via a light modulus or tadpole is shown to be severely constrained by astrophysical and cosmological data, leaving little room to accommodate and suggesting a need for refinements of the conjecture.

Abstract

The dS swampland conjecture , where 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 implies for form of the quintessence potential and couplings, where the weaker bound () is available for a specific type of quintessence whose couplings respect the equivalence principle, while the stronger bound () 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 , which results in a weaker bound on .

Paper Structure

This paper contains 7 sections, 63 equations, 2 figures.

Table of Contents

  1. introduction
  2. quintessence couplings to the standard model
  3. de Sitter swampland conjecture for the pion and Higgs extrema
  4. Pion extremum
  5. Higgs extremum
  6. Effects of the tadpole or runaway of additional scalar fields
  7. conclusion

Figures (2)

  • Figure 1: Observational upper bound on the modulus coupling $c_\chi=\tilde{d}_{\tilde{q}}+3\tilde{d}_g$ as a function of the modulus mass $m_\chi$. The gray regions are excluded by the blackhole superradiance (BH-SR) Arvanitaki:2014wva. The cyan region and the red region are excluded, respectively, by the composition-dependent Berge:2017ovySmith:1999cr and composition-independent Fischbach:1996eqArvanitaki:2014faa equivalence principle (CD-EP and CI-EP) tests. Constraints on the parametrized post-Newtonian (PPN) parameters Bertotti:2003rmHohmann:2013rbaScharer:2014kya exclude the blue region, which applies not only for a generic modulus, but also for a metrical modulus respecting the equivalence principle. The dark matter relic abundance constrains the modulus misalignment, excluding the brown region.
  • Figure 2: The refined upper bound on the parameter $c$ as a function of the mass $m_\chi$ of a modulus-like scalar field $\chi$ introduced to relax the original bounds (\ref{['eq:bound_gen']}) and (\ref{['eq:bound_met']}). This shows that the original bounds are not significantly relaxed by additional light scalar once the observational constraints on such light scalar are properly taken into account.