Quintessence Dark Energy from strongly-coupled Higgs mass gap: Local and
  Non-local higher-derivative non-perturbative scenarios
  We entertain the possibility that dark energy arises from the Higgs field of
quintessence type in the non-perturbative regimes. For this purpose we utilize
a set of exact solutions of Higgs field theory recently devised, in terms of
Jacobi elliptical function for a massless quartic scalar field, that satisfy a
massive dispersion relation. In certain regions of the parameter space,
determined by the quartic coupling value, we show that such solutions have the
property to give the correct behavior for the equation of state of the dark
energy depending on the initial $\theta$ value of periodicity of the Jacobi
elliptical function solution. It is seen that on a time scale determined by the
Hubble constant and the strength of the self-interaction of the scalar field,
when conformal invariance is restored, the equation of state for the dark
energy becomes manifest. Further we investigate scenarios within standard field
theory framework and also extending to higher-derivative theories, namely
infinite-derivative theory, motivated from p-adic string field theory, and
Lee-Wick theories and in all cases, we find suitable choices of the parameter
space leads to dark energy behavior of the Higgs field, which we compare.
