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 stuty the Starobinsky-type inflation model
in the framework of old-minimal supergravity, where the inflaton field in the
original (non-supersymmetric) Starobinsky inflation model becomes a complex
field. We study how the inflaton evolves on the two-dimensional field space,
varying the initial condition. 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 condition. Thus, the BICEP2 result strongly disfavors the complexified
Starobinsky inflation in supergravity.
