Jordan Frame Supergravity and Inflation in NMSSM

TL;DR

This paper develops a comprehensive supergravity framework in the Jordan frame with non-minimal coupling, applies it to NMSSM, and analyzes inflationary dynamics, revealing instabilities that necessitate model modifications.

Contribution

It provides an explicit supergravity action in the Jordan frame with non-minimal coupling and applies it to NMSSM Higgs inflation, identifying key stability issues.

Findings

The supergravity action in the Jordan frame is explicitly constructed.

NMSSM scalars can have canonical kinetic terms in this framework.

A tachyonic instability is found in the gauge singlet during inflation.

Abstract

We present a complete explicit N=1, d=4 supergravity action in an arbitrary Jordan frame with non-minimal scalar-curvature coupling of the form $\Phi(z, \bar z)\, R$. The action is derived by suitably gauge-fixing the superconformal action. The theory has a modified Kaehler geometry, and it exhibits a significant dependence on the frame function $\Phi (z, \bar z)$ and its derivatives over scalars, in the bosonic as well as in the fermionic part of the action. Under certain simple conditions, the scalar kinetic terms in the Jordan frame have a canonical form. We consider an embedding of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) gauge theory into supergravity, clarifying the Higgs inflation model recently proposed by Einhorn and Jones. We find that the conditions for canonical kinetic terms are satisfied for the NMSSM scalars in the Jordan frame, which leads to a simple action. However, we find that the gauge singlet field experiences a strong tachyonic instability during inflation in this model. Thus, a modification of the model is required to support the Higgs-type inflation.