The Volkov–Akulov–Starobinsky supergravity
I. Antoniadis (Department of Physics, CERN Theory Division, Geneva 23, CH-1211, Switzerland); E. Dudas (Centre de Physique Théorique, École Polytéchnique, Palaiseau, F-91128, France); S. Ferrara (INFN – Laboratori Nazionali di Frascati, Via Enrico Fermi 40, Frascati, I-00044, Italy, Department of Physics and Astronomy, University of California, Los Angeles, CA, 90095-1547, USA, Department of Physics, CERN Theory Division, Geneva 23, CH-1211, Switzerland); A. Sagnotti (Scuola Normale Superiore, INFN, Piazza dei Cavalieri 7, Pisa, I-56126, Italy)
We construct a supergravity model whose scalar degrees of freedom arise from a chiral superfield and are solely a scalaron and an axion that is very heavy during the inflationary phase. The model includes a second chiral superfield X , which is subject however to the constraint X2=0 so that it describes only a Volkov–Akulov goldstino and an auxiliary field. We also construct the dual higher-derivative model, which rests on a chiral scalar curvature superfield R subject to the constraint R2=0 , where the goldstino dual arises from the gauge-invariant gravitino field strength as γmnDmψn . The final bosonic action is an R+R2 theory involving an axial vector Am that only propagates a physical pseudoscalar mode.