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.
