Inflation, Supergravity and Superstrings

TL;DR

Inflation in N=1 supergravity typically induces a Hubble-scale inflaton mass, spoiling slow-roll. The paper derives a class of Kähler potentials and a constraint $W=W_\varphi=0$ during inflation with $W_\psi\neq0$ that cancel inflaton-dependent supergravity corrections, reducing the problem to a global SUSY-like potential. These forms arise naturally in string compactifications, and target-space dualities frequently include $R$-parities that enforce the necessary conditions. The resulting scenarios can yield a nearly scale-invariant spectrum with $n\approx 1-2/N\approx0.96$ and negligible tensor modes in many cases, while in others inflation persists even when the global SUSY limit would not, highlighting a robust connection between supergravity inflation and string theory constructions.

Abstract

The positive potential energy required for inflation spontaneously breaks supersymmetry and in general gives any would-be inflaton an effective mass of order the inflationary Hubble parameter thus ruling it out as an inflaton. In this paper I give simple conditions on the superpotential that eliminate some potential sources for this mass, and derive a form for the Kahler potential that eliminates the rest. This reduces the problem of constructing a model of inflation in supergravity to that of constructing one in global supersymmetry with the extra conditions $W=W_\varphi=ψ=0$ during inflation (where $W$ is the superpotential, the inflaton $\in\varphi$, and $W_ψ\neq0$). I then point out that Kahler potentials of the required form often occur in superstrings and that the target space duality symmetries of superstrings often contain R-parities which would make $W=W_\varphi=0$ automatic for $ψ=0$.