Cancellation of loop corrections to soft scalar power spectrum

We prove the absence of scale-invariant one-loop corrections to the superhorizon curvature perturbations from small-scale (potentially enhanced) scalar perturbations in a general inflationary setup, including the transient ultra-slow-roll scenario. We demonstrate this by analyzing the symmetry structure of an in-in effective field theory for the soft curvature perturbations, and by explicitly performing one-loop calculations, integrating out hard modes in the soft limit of external momenta. The dilatation symmetry, respected by a counter term necessary for the tadpole cancellation, guarantees the cancellation of scale-invariant corrections.