Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approach

Abstract

We revisit one-loop corrections to the power spectrum of curvature perturbations $\zeta$ in an inflationary scenario containing a transient ultra-slow-roll (USR) period. In Ref.[1], it was argued that one-loop corrections to the power spectrum of $\zeta$ can be larger than the tree-level one within the parameter region generating the seeds of primordial black holes during the USR epoch, which implies the breakdown of perturbation theory. We prove that this is not the case by using a master formula for one-loop corrections to the power spectrum obtained in Ref.[2]. We derive the same formula within the path-integral formalism, which is simpler than the original derivation in [2]. To show the smallness of one-loop corrections, the consistency relations and the effective constancy of tree-level mode functions of $\zeta$ for super-Hubble modes play essential roles, with which the master formula gives a simple expression for one-loop corrections. For concreteness, we provide a reduced set of interactions including the leading-order one, while establishing the consistency relations in a self-consistent manner. We also show how the consistency relations of various operators hold explicitly, which plays a key role in proving the absence of large one-loop corrections.

47 pages, 11 figures

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Cited by in corpus (12)

• Ultra-Slow-Roll Inflation on the Lattice I: Backreaction and Nonlinear Effects
• Absence of one-loop effects on large scales from small scales in non-slow-roll dynamics II: Quartic interactions and consistency relations
• Absence of one-loop effects on large scales from small scales in non-slow-roll dynamics
• Conservation of superhorizon curvature perturbations at one loop: Backreaction in the in-in formalism and Renormalization
• Incorporating Backreaction in One-Loop Corrections in Ultra-Slow-Roll Inflation
• Role of the counterterms in the conservation of superhorizon curvature perturbations at one loop
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