The Minimal Volkov - Akulov - Starobinsky Supergravity

TL;DR

The paper presents a minimal, universal embedding of Starobinsky inflation in N=1 supergravity by combining a constrained goldstino multiplet X (with $X^2=0$) and a chiral inflaton T. It derives a two-derivative formulation with K = -3 log(T+Tbar - X Xbar) and W = M X T + f X + W0, yielding a Starobinsky-like potential in which the axion is heavy during inflation. It also constructs a dual higher-derivative gravitational theory with a constrained curvature superfield ${\cal R}$ satisfying ${\cal R}^2 = 0$, and shows the two descriptions are equivalent off-shell. The resulting bosonic sector is an $R+R^2$ theory with an axial vector that propagates a single pseudoscalar, linking the nilpotent goldstino sector to the gravitational degrees of freedom and providing a clean, minimal route to Starobinsky inflation in 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 ${\cal R}$ subject to the constraint ${\cal R}^2=0$, where the goldstino dual arises from the gauge - invariant gravitino field strength as $γ^{mn} {\cal D}_m ψ_n$. The final bosonic action is an $R+R^2$ theory involving an axial vector $A_m$ that only propagates a physical pseudoscalar mode.