$R^n$ Extension of Starobinsky Model in Old Minimal Supergravity

We provide a succinct way to construct the supersymmetric completion of $R^n$ $(n\ge 3)$ 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.