  We derive a general criterion that defines all single-field models leading to
Starobinsky-like inflation and to universal predictions for the spectral index
and tensor-to-scalar ratio, which are in agreement with Planck data. Out of all
the theories that satisfy this criterion, we single out a special class of
models with the interesting property of retaining perturbative unitarity up to
the Planck scale. These models are based on induced gravity, with the Planck
mass determined by the vacuum expectation value of the inflaton.
