The Minimal Volkov - Akulov - Starobinsky Supergravity
  We construct a supergravity model whose scalar degrees of freedom arise from a chiral superfield and are solely a scalaron and an axion that is very heavy during the inflationary phase. The model includes a second chiral superfield $X$, which is subject however to the constraint $X^2=0$ so that it describes only a Volkov - Akulov goldstino and an auxiliary field. We also construct the dual higher - derivative model, which rests on a chiral scalar curvature superfield ${\cal R}$ subject to the constraint ${\cal R}^2=0$, where the goldstino dual arises from the gauge - invariant gravitino field strength as $\gamma^{mn} {\cal D}_m \psi_n$. The final bosonic action is an $R+R^2$ theory involving an axial vector $A_m$ that only propagates a physical pseudoscalar mode. 
I. Antoniadis (CERN), E. Dudas (CphT - Ecole Polytechnique), S.   Ferrara (CERN), A. Sagnotti (Scuola Normale Superiore and ...
hep-th astro-ph.CO gr-qc hep-ph