Absence of one-loop effects on large scales from small scales in non-slow-roll dynamics

Abstract

We question the existence of one-loop corrections to the large-scale power spectrum from small-scale modes in non-slow-roll dynamics which are not volume suppressed by the ratio of the short to long distance scales. One-loop contributions proportional to the long wavelength tree-level power spectrum, and not sharing this suppression, have appeared in studies involving interactions singled out by the non-slow-roll dynamics. In this context, we show the relevance of seemingly irrelevant interactions terms, such as the one provided by total derivative terms (boundary terms), and how they equally lead to non-volume suppressed contributions and exact cancellations.

19 pages. v2: Substantial updates; see "Note added" in the main text. v3: Expanded discussion in Sec. 2 on equivalent Hamiltonians; version published in JHEP

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• Incorporating Backreaction in One-Loop Corrections in Ultra-Slow-Roll Inflation
• Ultra-Slow-Roll Inflation on the Lattice II: Nonperturbative Curvature Perturbation
• Stochastic Inflation with Interacting Noises
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
• Separate universe in multifield inflation: a phase-space approach