Cosmology of Linear Higgs-Sigma Models with Conformal Invariance

TL;DR

This paper explores linear Higgs-sigma models with conformal invariance, incorporating higher curvature terms to unify Higgs inflation and dark energy models, and discusses implications for vacuum stability.

Contribution

It introduces a class of linear Higgs-sigma models with conformal symmetry that incorporate higher curvature terms, linking inflation and dark energy.

Findings

Successful inflation is achieved with sigma fields derived from $R^2$ terms.

Dark energy tracker solutions are possible with $R^{p+1}$ terms for $-1<p<0$.

Implications for Higgs interactions and vacuum stability are discussed.

Abstract

We consider general linear Higgs-sigma models as ultra-violet completions of the Higgs inflation. We introduce general higher curvature terms beyond Einstein gravity and recast them into a class of linear Higgs-sigma models in the scalar-dual formulation where conformal symmetry is manifest. Integrating out the sigma field in this class of linear sigma models, we obtain the same Higgs inflation Lagrangian of non-linear sigma model type in the effective theory. We show that the successful inflation for sigma field singles out the sigma-field potential derived from the $R^2$ term and the tracker solution for dark energy at late times can be realized for the $R^{p+1}$ term with $-1<p<0$. We also discuss the implications of Higgs-sigma interactions for the inflation and the vacuum stability in the Standard Model.