A geometric bound on F-term inflation

TL;DR

This paper derives a geometric bound on F-term inflation within minimal $N=1$ supergravity by projecting the scalar mass matrix onto the sGoldstini directions tied to SUSY breaking. The bound expresses an upper limit on the second slow-roll parameter $\eta$ in terms of the first parameter $\epsilon$, the ratio $\gamma = \frac{\ell_p^2 V}{3 |m_{3/2}|^2}$, and the sectional curvature $\tilde{\mathcal{R}}$ of the sGoldstini plane on the Kähler manifold. Two regimes emerge: for $0<\gamma\leq 4/3$, a compatible realization of slow-roll, effective single-field inflation with possible non-canonical kinetics can occur in some cases; for $\gamma>4/3$, only two of the three conditions (slow-roll, single-field, canonical kinetic terms) can be satisfied, favoring large-field inflation and potential tensor modes. The results constrain many existing models, imply necessary negative curvature in the Kähler geometry for certain realizations, and connect to recent work on sGoldstino inflation, suggesting that sub-Hubble gravitino mass scenarios tend to favor large-field dynamics with observable gravitational waves.

Abstract

We discuss a general bound on the possibility to realise inflation in any minimal supergravity with F-terms. The derivation crucially depends on the sGoldstini, the scalar field directions that are singled out by spontaneous supersymmetry breaking. The resulting bound involves both slow-roll parameters and the geometry of the Kähler manifold of the chiral scalars. We analyse the inflationary implications of this bound, and in particular discuss to what extent the requirements of single field and slow-roll can both be met in F-term inflation.