Complexified Starobinsky inflation in supergravity in the light of recent BICEP2 result

Motivated by the recent observation of the B-mode signal in the cosmic microwave background by BICEP2, we study the Starobinsky-type inflation model in the framework of old-minimal supergravity, where the inflaton field in the original (non-supersymmetric) Starobinsky inflation model is promoted to a complex field. We study how the inflaton evolves on the two-dimensional field space, varying the initial conditions. We show that (i) one of the scalar fields has a very steep potential once the trajectory is off from that of the original Starobinsky inflation, and that (ii) the B-mode signal observed by BICEP2 is too large to be consistent with the prediction of the model irrespective of the initial conditions. Thus, the BICEP2 result strongly disfavors the complexified Starobinsky inflation in supergravity.