$R^n$ Extension of Starobinsky Model in Old Minimal Supergravity
  We provide a succinct way to construct the supersymmetric completion of $R^n$
$(n\ge3)$ in components using superconformal formulation of old minimal
supergravity. As a consequence, we obtain the polynomial $f(R)$ supergravity
extending the supersymmetric Starobinsky model to any higher power of $R$. The
supersymmetric vacua in polynomial $f(R)$ supergravity are studied. We also
present the $R^n$ extended Minimal Volkov-Akulov-Starobinsky Model.
