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

Primordial perturbations from ultra-slow-roll single-field inflation with quantum loop effects