  The general scalar-tensor theory that includes all the dimension-four terms
has parameter regions that can produce successful inflation consistent with
cosmological observations. This theory is in fact the same as the
Higgs-Starobinsky inflation, when the scalar is identified with the Standard
Model Higgs boson. We consider possible dimension-six operators constructed
from non-derivative terms of the scalar field and the Ricci scalar as
perturbations. We investigate how much suppression is required for these
operators to avoid disrupting the successful inflationary predictions. To
ensure viable cosmological predictions, the suppression scale for the sixth
power of the scalar should be as high as the Planck scale. For the other terms,
much smaller scales are sufficient.
