Rⁿ extension of the Starobinsky model in old minimal supergravity

We provide a succinct way to construct the supersymmetric completion of Rⁿ (n⩾3) in components using the 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 Rⁿ extended minimal Volkov–Akulov–Starobinsky model. (paper)