Revisiting Loop Corrections in Single Field USR Inflation

Abstract: We revisit the one-loop corrections on CMB scale perturbations induced from small scale modes in single field models which undergo a phase of ultra slow-roll inflation. There were concerns that large loop corrections are against the notion of the decoupling of scales and they are cancelled out once the boundary terms are included in Hamiltonian. We highlight that the non-linear coupling between the long and short modes and the modulation of the short mode power spectrum by the long mode are the key physical reasons behind the large loop corrections. In particular, in order for the modulation by the long mode to be significant there should be a strong scale-dependent enhancement in power spectrum of the short mode which is the hallmark of the USR inflation. We highlight the important roles played by the would-be decaying mode which were not taken into account properly in recent works claiming the loop cancellation. We confirm the original conclusion that the loop corrections are genuine and they can be dangerous for PBHs formation unless the transition to the final attractor phase is mild.