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 R + R-2 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 R + R-2 supergravity, to a scale invariant R-2 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.