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 + 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 = −α log(T + T ) for 3 ≤ α 6.37 can accomodate Starobinsky-like inflation with the universal prediction n s 1 − 2 Ne and r 4α (α−2) 2 N 2 e , while for 6.37 α 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:2001.06617v3 [hep-th] 12 Mar 20201 Recently an alternative approach (without nilpotent superfields) to Volkov-Akulov supergravity in de Sitter space was proposed, that uses unimodular supergravity [30,31].2 Although the original potential has tachyonic instability at C = 0, it can be removed by adding quartic correction ∼ |C| 4 to the Kähler potential (3), as was shown in Ref. [36].3 In Ref.[9] the authors also propose a different class of Volkov-Akulov-Starobinsky supergravity models where the Kähler potential has the simplest shift-symmetric form, K = (T + T ) 2 /2.