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 X2=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 R subject to the constraint R2=0, where the goldstino dual arises from the gauge-invariant gravitino field strength as γmnDmψn. The final bosonic action is an R+R2 theory involving an axial vector Am that only propagates a physical pseudoscalar mode.
Highlights
It was recently shown how to embed in Supergravity [1] a class of models [2] including the Starobinsky potential [3], which affords an excellent agreement with recent PLANCK data [4] for an inflationary epoch of about 60 e–folds
The models based on the “old minimal” supergravity rest on a pair of chiral superfields, and involve three scalar fields in addition to the inflaton
The construction reflects the Starobinsky duality [3, 8] between an R + R2 action and a special scalar–gravity system, encompassed by the master action
Summary
It was recently shown how to embed in Supergravity [1] a class of models [2] including the Starobinsky potential [3], which affords an excellent agreement with recent PLANCK data [4] for an inflationary epoch of about 60 e–folds. The Lagrangian (1.12) contains Starobinsky’s inflaton φ, which is related to T according to Re(T ) = exp 2/3 φ , and setting to zero the other three fields one can recover exactly, for W0 = 0, the scalar potential of the original Starobinsky model. It was shown in [5] that for a minimal choice h(C, C) = CC the complex scalar direction C is unstable during the inflationary phase.
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