  It is known that the single-field inflation with a transient ultra-slow-roll
phase can produce a large curvature perturbation at small scales for the
formation of primordial black holes. In our previous work, we have considered
quantum loop corrections to the curvature perturbation and found that the
growth of these small-scale modes would affect the curvature perturbation at
large scales probed by cosmic microwave background observation. In this work,
we will further derive the constraints on the growing modes in the transition
between the slow-roll and the ultra-slow-roll phases under the effect of the
loop corrections. Our results would help clarify the recent controversy on
whether or not the primordial-black-hole formation from the single-field
inflation is ruled out at one-loop level.
