Inflation with Non-minimal Gravitational Couplings and Supergravity

TL;DR

This work investigates whether a large non-minimal coupling to gravity can drive inflation within a supersymmetric framework. By embedding the non-minimal interaction in supergravity via a holomorphic function $X(\Phi)$, the authors compare the MSSM and NMSSM. They show that the MSSM cannot realize slow-roll inflation in this setup, whereas the NMSSM with a singlet and a Higgs-doublet–driven non-minimal coupling can produce a viable slow-roll inflationary trajectory along the $D$-flat Higgs direction, with characterized slow-roll parameters $\epsilon$ and $\eta$ and a calculable number of e-folds $N$. For a representative choice $\chi \sim 5\times10^{4}$, inflation ends near $h_{end}\sim7\times10^{-3}M_P$, illustrating a concrete SUSY/SUGRA realization of Higgs-driven inflation. The authors also note important open questions about effective field theory validity and renormalization-group effects that warrant further study, especially in the context of RG running and possible GUT embeddings.

Abstract

We explore in the supergravity context the possibility that a Higgs scalar may drive inflation via a non-minimal coupling to gravity characterised by a large dimensionless coupling constant. We find that this scenario is not compatible with the MSSM, but that adding a singlet field (NMSSM, or a variant thereof) can very naturally give rise to slow-roll inflation. The inflaton is necessarily contained in the doublet Higgs sector and occurs in the D-flat direction of the two Higgs doublets.