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

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