Higher Curvature Supergravity and Cosmology

In this contribution we describe dual higher-derivative formulations of some cosmological models based on supergravity. Work in this direction started with the Starobinsky model, whose supersymmetric extension was derived in the late 80's and was recently revived in view of new CMB data. Models dual to higher-derivative theories are subject to more restrictions than their bosonic counterparts or standard supergravity. The three sections are devoted to a brief description of supergravity, to a scale invariant R2 Supergravity and to theories with a nilpotent curvature, whose duals describe non-linear realizations (in the form of a Volkov-Akulov constrained superfield) coupled to supergravity