Inflation, supergravity, and superstrings

Simple conditions on the superpotential are given that eliminate some potential sources for this mass, and derive a form for the K\"ahler potential that eliminates the rest.

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 $W=W_\varphi=\psi=0$ during inflation (where $W$ is the superpotential, the inflaton $\in\varphi$, and $W_\psi\neq0$). 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 $\psi=0$.