Higher order corrections in minimal supergravity models of inflation

We study higher order corrections in new minimal supergravity models of a single scalar field inflation. The gauging in these models leads to a massive vector multiplet and the D-term potential for the inflaton field with a coupling g² ∼ 10^-10. In the de-Higgsed phase with vanishing g², the chiral and vector multiplets are non-interacting, and the potential vanishes. We present generic manifestly supersymmetric higher order corrections for these models. In particular, for a supersymmetric gravity model -R+R² we derive manifestly supersymmetric corrections corresponding to Rⁿ. The dual version corresponds to a standard supergravity model with a single scalar and a massive vector. It includes, in addition, higher Maxwell curvature/scalar interaction terms of the Born-Infeld type and a modified D-term scalar field potential. We use the dual version of the model to argue that higher order corrections do not affect the last 60 e-foldings of inflation; for example the ξR⁴ correction is irrelevant as long as ξ < 10²⁴.