CLASSICAL AND QUANTUM GRAVITY, cilt.31, sa.20, 2014 (SCI-Expanded)
We provide a succinct way to construct the supersymmetric completion of R-n (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 R-n extended minimal Volkov-Akulov-Starobinsky model.