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

Understand

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.