Meaning of the field dependence of the renormalization scale in Higgs
  inflation
  We consider the prescription dependence of the Higgs effective potential
under the presence of general nonminimal couplings. We evaluate the fermion
loop correction to the effective action in a simplified Higgs-Yukawa model
whose path integral measure takes simple form either in the Jordan or Einstein
frame. The resultant effective action becomes identical in both cases when we
properly take into account the quartically divergent term coming from the
change of measure. Working in the counterterm formalism, we clarify that the
difference between the prescriptions I and II comes from the counter term to
cancel the logarithmic divergence. This difference can be absorbed into the
choice of tree-level potential from the infinitely many possibilities,
including all the higher-dimensional terms. We also present another mechanism
to obtain a flat potential by freezing the running of the effective quartic
coupling for large field values, using the nonminimal coupling in the gauge
kinetic function.
