Conservation of superhorizon curvature perturbations at one loop: Backreaction in the in-in formalism and Renormalization

TL;DR

This paper demonstrates that superhorizon curvature perturbations remain conserved at one-loop in single-field inflation, emphasizing the importance of backreaction and renormalization in the in-in formalism.

Contribution

It provides a detailed analysis of backreaction effects and UV divergence renormalization, establishing conditions for conservation of curvature perturbations at one-loop.

Findings

Superhorizon curvature perturbations are conserved at one-loop in certain inflation models.

Backreaction significantly influences the conservation unless counter terms are tuned.

Explicit renormalization of UV divergences is achieved using the in-in formalism.

Abstract

We show that the superhorizon-limit curvature perturbations are conserved at one-loop level in single-field inflation models with a transient non-slow-roll period. We take the spatially-flat gauge, where the backreaction plays a crucial role for the conservation of superhorizon curvature perturbations unless the counter terms are tuned. We calculate the backreaction with the in-in formalism. In addition, we explicitly show the renormalization of the UV divergences with the counter terms.