Large gauge transformation, Soft theorem, and Infrared divergence in inflationary spacetime

TL;DR

This paper explores the connection between large gauge transformations, the soft theorem, and infrared divergences in inflationary spacetime, emphasizing the importance of locality conditions for these IR properties and their applicability to systems with heavy and higher spin fields.

Contribution

It demonstrates that locality conditions are essential for establishing the IR properties like the consistency relation and divergence cancellation, extending the analysis to systems with heavy and higher spin fields.

Findings

Locality condition is crucial for IR consistency relations.

Locality guarantees cancellation of IR divergences in observable-like variables.

The framework applies to systems with heavy fields and higher spins, including string theory motivated models.

Abstract

It is widely known that the primordial curvature perturbation $\zeta$ has several universal properties in the infrared (IR) such as the soft theorem, which is also known as the consistency relation, and the conservation in time. They are valid in rather general single clock models of inflation. It has been argued that these universal properties are deeply related to the large gauge transformations in inflationary spacetime. However, the invariance under the large gauge transformations is not sufficient to show these IR properties. In this paper, we show that the locality condition is crucial to show the consistency relation and the conservation of $\zeta$. This argument also can apply to an interacting system with the inflaton and heavy fields which have arbitrary integer spins, including higher spin fields, which may be motivated from string theory. We will also show that the locality condition guarantees the cancellation of the IR divergences in a certain class of variables whose correlation functions resemble cosmologically observable quantities.