Quintessence saves Higgs instability

We study a model where quintessence potential e−ξϕ coupled to Higgs potential. We calculate the evolution of the quintessence, and track the running of the effective Higgs self coupling. We find it slightly larger than that of the standard model in the past. Requiring the electroweak vacuum to be absolutely stable in inflationary era, we find a lower bound ξ>0.35±0.05, where the uncertainty is mainly from the measurement of the top quark mass. This lower bound, together with the upper bound from the observation for dark energy ξ≲0.6, narrows down the parameter space and makes it possible to test this model in the near future. Interestingly, the bound on ξ, if actually shown to be the case by observation, supports the recently proposed Swampland Conjecture.