In this talk we describe dual higher derivative formulations of some cosmological models based on supergravity. Work in this direction started with the R + R2 Starobinsky model, whose supersymmetric extension was derived in the late 80s 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 duals. We will start with a brief description of R + R2 supergravity, then a scale invariant R2 Supergravity and finally theories with a nilpotent curvature, whose duals describe non-linear realizations (in the form a Volkov-Akulov constrained superfield) coupled to supergravity.