Loops in inflationary correlation functions

TL;DR

This paper reviews recent advances in understanding loop corrections in inflationary correlation functions, emphasizing the importance of gauge invariance and the restrictions on quantum states to ensure IR regularity and predictive power.

Contribution

It clarifies the origin of IR divergences in inflationary loops and proposes conditions for IR regularity across different perturbation types, highlighting the role of observable quantities.

Findings

IR divergences are linked to gauge invariance issues.

Proper identification of observable quantities ensures IR regularity.

Restrictions on quantum states are necessary for IR regularity.

Abstract

We review the recent progress regarding the loop corrections to the correlation functions in the inflationary universe. A naive perturbation theory predicts that loop corrections generated during inflation suffer from various infrared (IR) pathologies. Introducing an IR cutoff by hand is not only unsatisfactory but also does not fix the problem of secular growth, which may ruin the predictive power of inflation models if the inflation lasts sufficiently long. We discuss the origin of the IR divergences and explore the regularity conditions of loop corrections for the adiabatic perturbation, the iso-curvature perturbation, and the tensor perturbation, in turn. These three kinds of perturbations have qualitative differences, but in discussing the IR regularity there is a feature common to all cases, which is the importance of the proper identification of observable quantities. Genuinely observable quantities should respect the gauge invariance from the view point of a local observer. Interestingly, we find that the requirement of the IR regularity restricts the allowed quantum states.