The Minimal Volkov - Akulov - Starobinsky Supergravity

Abstract

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 $X^2=0$ 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 $\mathcal{R}$ subject to the constraint ${\mathcal{R}}^2=0$, where the goldstino dual arises from the gauge - invariant gravitino field strength as ${\gamma }^{mn}{\mathcal{D}}_m{\psi }_n$. The final bosonic action is an $R+R^2$ theory involving an axial vector $A_m$ that only propagates a physical pseudoscalar mode.

Comments: 9 pages, LaTeX. Title shortened, references added. To appear in Phys. Lett. B