Volkov-Akulov-Starobinsky supergravity revisited

Abstract

We find new realizations of Volkov-Akulov-Starobinsky supergravity, i.e. Starobinsky inflationary models in supergravity coupled to a nilpotent superfield describing Volkov-Akulov goldstino. Our constructions are based on the no-scale Kähler potential $K=-3\log (T+\bar{T})$ for the inflaton field, and can describe de Sitter vacuum after inflation where supersymmetry is broken by the goldstino auxiliary component. In fact, we show that a more general class of models with $K=-\alpha \log (T+\bar{T})$ for $3\le \alpha \lesssim 6.37$ can accomodate Starobinsky-like inflation with the universal prediction $n_s\simeq 1-\frac{2}{N_e}$ and $r\simeq \frac{4\alpha }{(\alpha -2{)}^2{N}_e^2}$, while for $6.37\lesssim \alpha \lesssim 7.23$ viable hilltop inflation is possible (with $n_s$ and $r$ close to the above expressions). We derive the full component action and the masses of sinflaton, gravitino, and inflatino that are generally around the inflationary Hubble scale. Finally, we show that one of our models can be dualized into higher-derivative supergravity with constrained chiral curvature superfield.

arXiv comment18 pages, 3 figures (5 subfigures). Update (v3): added new section describing dual (higher-derivative) gravitational actions

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• Nilpotent superfields for broken abelian symmetries
• Starobinsky Inflation with T-Model Kaehler Geometries
• Rapid-turn inflation in supergravity is rare and tachyonic