Volkov\u2013Akulov\u2013Starobinsky 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=-3log (T+overline{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+overline{T}) for 3le alpha lesssim 6.37 can accomodate Starobinsky-like inflation with the universal prediction n_ssimeq 1-frac{2}{N_e} and rsimeq frac{4alpha }{(alpha -2)^2N_e^2}, while for 6.37lesssim 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.