Supergravity Higgs Inflation and Shift Symmetry in Electroweak Theory

TL;DR

This paper develops a supergravity-based Higgs inflation model within the NMSSM, resolving previous instabilities through a shift symmetry in the Kähler potential, and connects inflationary predictions with axion searches.

Contribution

It introduces a novel shift symmetry in the Kähler potential of the NMSSM Higgs sector to enable successful inflation without the $ ext{eta}$-problem.

Findings

The model avoids tachyonic instability during inflation.

It predicts a viable inflationary scenario in the NMSSM, especially in the PQ limit.

The model's viability can be tested via CMB observations and axion searches.

Abstract

We present a model of inflation in a supergravity framework in the Einstein frame where the Higgs field of the next to minimal supersymmetric standard model (NMSSM) plays the role of the inflaton. Previous attempts which assumed non-minimal coupling to gravity failed due to a tachyonic instability of the singlet field during inflation. A canonical K\"{a}hler potential with \textit{minimal coupling} to gravity can resolve the tachyonic instability but runs into the $\eta$-problem. We suggest a model which is free of the $\eta$-problem due to an additional coupling in the K\"{a}hler potential which is allowed by the Standard Model gauge group. This induces directions in the potential which we call K-flat. For a certain value of the new coupling in the (N)MSSM, the K\"{a}hler potential is special, because it can be associated with a certain shift symmetry for the Higgs doublets, a generalization of the shift symmetry for singlets in earlier models. We find that K-flat direction has $H_u^0=-H_d^{0*}.$ This shift symmetry is broken by interactions coming from the superpotential and gauge fields. This direction fails to produce successful inflation in the MSSM but produces a viable model in the NMSSM. The model is specifically interesting in the Peccei-Quinn (PQ) limit of the NMSSM. In this limit the model can be confirmed or ruled-out not just by cosmic microwave background observations but also by axion searches.