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

TL;DR

This paper investigates the implications of the dS swampland conjecture on electroweak and QCD symmetry breaking potentials, deriving stringent bounds on the conjecture's parameter from the existence of dS extrema in these potentials.

Contribution

It provides the first detailed analysis of how the dS swampland conjecture constrains low-energy potentials like Higgs and pion, especially at their dS extrema.

Findings

Pion dS extremum constrains c to be less than about 10^{-2} to 10^{-5}.

Weaker bounds are obtained for the Higgs extremum.

Additional scalar fields do not significantly relax the bounds due to observational constraints.

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 $\cos(\pi_0/f_\pi)=-1$ 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 $c$.