Cosmology of Linear Higgs-Sigma Models with Conformal Invariance

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.

Inflation and Supersymmetry Breaking in Higgs-$R^2$ Supergravity

“…Now, we fix the dilatation gauge by X 0 = 1 + 1 √ 6 σ, where σ is a function of ẑI and z J . In particular, we choose σ so that it satisfies the following constraint [19],…”

“…In this regard, the possibility of combining the Higgs and Starobinsky models has been revisited due to the presence of the dual scalar field, scalaron, in the Starobinsky model [13,14]. Indeed, it has been shown that the scalaron or sigma field in the linearized action, in the Starobinsky model, unitarizes the Higgs inflation up to the Planck scale [15][16][17][18][19]. There are more general sigma models unitarizing the Higgs inflation [19] beyond the Starobinsky model.…”

“…Indeed, it has been shown that the scalaron or sigma field in the linearized action, in the Starobinsky model, unitarizes the Higgs inflation up to the Planck scale [15][16][17][18][19]. There are more general sigma models unitarizing the Higgs inflation [19] beyond the Starobinsky model.…”

“…We also discuss the importance of the equivalent frames describing the same physics, because some symmetries and critical problems can be made more clear in one frame than in the other. In the sigma-model frame for Higgs inflation where the conformal symmetry is manifest, the Higgs kinetic term can be recast into a non-linear model type [17,19], so the unitarity problem can be seen clearly from the non-canonical form of the Higgs kinetic terms [8,10]. Moreover, in the presence of the R 2 term in the Higgs inflation, the dual-scalar field for the R 2 term, called the sigma field, appears to respect the conformal symmetry and internal symmetries in the sigma-model frame, so unitarity becomes manifest [17,19].…”

“…In the sigma-model frame for Higgs inflation where the conformal symmetry is manifest, the Higgs kinetic term can be recast into a non-linear model type [17,19], so the unitarity problem can be seen clearly from the non-canonical form of the Higgs kinetic terms [8,10]. Moreover, in the presence of the R 2 term in the Higgs inflation, the dual-scalar field for the R 2 term, called the sigma field, appears to respect the conformal symmetry and internal symmetries in the sigma-model frame, so unitarity becomes manifest [17,19]. We introduce the equivalent frames for the Higgs-sigma inflation in a manifestly supersymmetric way in conformal supergravity [34][35][36][37][38], thanks to a large gauge symmetry.…”