General inflaton potentials in supergravity

TL;DR

This work shows that in N = 1 supergravity one can realize essentially any slow-roll inflaton potential V(φ) by adopting W = S f(Φ) with f real holomorphic and by carefully engineering the Kähler geometry to stabilize extra fields along the inflationary trajectory. The main result is that V(φ) = f^2(Re Φ), so an arbitrary V is achieved by choosing f accordingly, while the stabilization is controlled by Kähler curvature projections onto the goldstino direction; explicit Kähler potentials and a covariant formulation clarify how to ensure heavy orthogonal fields or, alternatively, enable curvaton-type scenarios with light additional fields. This framework provides a flexible, geometrically controlled path to single-field inflation within supergravity, with clear criteria for stability and potential extensions to non-Gaussianity through light fields.

Abstract

We describe a way to construct supergravity models with an arbitrary inflaton potential V (φ) and show that all other scalar fields in this class of models can be stabilized at the inflationary trajectory by a proper choice of the Kähler potential.