  We elaborate on the predictions of the imaginary Starobinsky model of
inflation coupled to matter, where the inflaton is identified with the
imaginary part of the inflaton multiplet suggested by the Supergravity
embedding of a pure R + R^2 gravity. In particular, we study the impact of
higher-order curvature terms and show that, depending on the parameter range,
one may find either a quadratic model of chaotic inflation or monomial models
of chaotic inflation with fractional powers between 1 and 2.
