Quintessence Dark Energy from strongly-coupled Higgs mass gap: Local and Non-local higher-derivative non-perturbative scenarios

TL;DR

This paper explores the idea that dark energy can originate from the Higgs field in non-perturbative regimes, using exact solutions and higher-derivative theories to model its equation of state and behavior over cosmic time.

Contribution

It introduces novel exact solutions of the Higgs field in non-perturbative regimes and extends the analysis to higher-derivative theories, providing new models for dark energy.

Findings

Higgs field solutions can produce the correct dark energy equation of state

Higher-derivative theories can replicate dark energy behavior

Parameter choices influence the transition to conformal invariance

Abstract

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.