Multi-soft theorems for cosmological correlators: Background wave method for scalars & gravitons

TL;DR

This paper derives multi-soft theorems for cosmological correlators using the background wave method, providing a tool to test inflationary models through consistency relations.

Contribution

It introduces tree-level multi-soft theorems for scalars and gravitons, incorporating soft-exchange contributions via the background wave approach.

Findings

Derived leading-order multi-soft theorems for scalars and tensors.

Included soft-exchange effects such as tensor exchanges in scalar correlators.

Provided a framework to test inflationary models through consistency relations.

Abstract

Cosmological soft theorems (or consistency relations) provide a powerful probe for the physics of inflation. These relations rely on minimal assumptions and hold very generally. Consequently, any violation of these relations would rule out a large class of inflationary models. For instance, a violation of the scalar soft theorem (or consistency relation) would rule out all attractor single-field inflation models and instead point toward either multi-field dynamics or a non-attractor phase. In this paper, we derive tree-level multi-soft theorems, at leading order in the soft expansion, for both scalar and tensor correlation functions. Our analysis employs the background-wave method, in which the effect of long-wavelength modes is captured by an appropriate spatial coordinate rescaling. In addition, we systematically incorporate soft-exchange contributions, including tensor exchanges in scalar correlators and scalar exchanges in tensor correlators.