Inflation, supergravity, and superstrings

Abstract

The positive potential energy required for inflation spontaneously breaks supersymmetry and in general gives any would-be inflaton an effective mass of the order of 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 K\"ahler 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=${\mathit{W}}_{\mathit{c}\mathit{p}\mathit{h}\mathit{i}}$=\ensuremath{\psi}=0 during inflation (where W is the superpotential, the inflaton \ensuremath{\in}cphi, and ${\mathit{W}}_{\mathrm{\ensuremath{\psi}}}$\ensuremath{\ne}0). I then point out that K\"ahler 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=${\mathit{W}}_{\mathit{c}\mathit{p}\mathit{h}\mathit{i}}$=0 automatic for \ensuremath{\psi}=0.