Chaotic inflation in Jordan frame supergravity

TL;DR

The paper shows that chaotic inflation with a large non-minimal coupling in Jordan-frame supergravity suffers from a tachyonic instability in the non-inflaton direction. It proposes a radiatively generated higher-order frame-function correction $\Delta\Omega=-\gamma(X^\dagger X)^2$ from heavy thresholds to stabilize the X-direction without perturbing the inflaton dynamics, yielding a tachyon-free slow-roll regime under the condition $\gamma>0.003$ (for typical values of the inflaton trajectory). This mechanism reproduces inflationary observables compatible with COBE normalization and unitarity bounds, and it extends naturally to Higgs inflation in the NMSSM by addressing the NMSSM-specific tachyon and allowing for a viable $\mu$ term and gravitino DM in gauge-mediated scenarios. The results connect high-scale inflationary dynamics to NMSSM phenomenology, with distinctive implications for the Higgs sector and dark matter, while inviting further work on loop corrections during inflation.

Abstract

We consider the inflationary scenario with non-minimal coupling in 4D Jordan frame supergravity. We find that there occurs a tachyonic instability along the direction of the accompanying non-inflaton field in generic Jordan frame supergravity models. We propose a higher order correction to the Jordan frame function for solving the tachyonic mass problem and show that the necessary correction can be naturally generated by the heavy thresholds without spoiling the slow-roll conditions. We discuss the implication of the result on the Higgs inflation in NMSSM.