Soft Theorems For Shift-Symmetric Cosmologies

TL;DR

This paper derives soft theorems for shift-symmetric single-clock cosmologies, providing consistency conditions that determine the behavior of correlators with a soft scalar mode, and applies these to Ultra-slow-roll inflation.

Contribution

It introduces new soft theorems combining diffeomorphism and shift-symmetry, extending the understanding of infrared structures in shift-symmetric cosmologies.

Findings

Reproduces the squeezed bispectrum for Ultra-slow-roll inflation.

Shows that shift-symmetry leads to specific consistency conditions.

Provides insights into the infrared structure of single-clock spacetimes.

Abstract

We derive soft theorems for single-clock cosmologies that enjoy a shift symmetry. These so-called consistency conditions arise from a combination of a large diffeomorphism and the internal shift-symmetry and fix the squeezed limit of all correlators with a soft scalar mode. As an application, we show that our results reproduce the squeezed bispectrum for Ultra-slow-roll inflation, a particular shift-symmetric, non-attractor model which is known to violate Maldacena's consistency relation. Similar results have been previously obtained by Mooij and Palma using background-wave methods. Our results shed new light on the infrared structure of single-clock cosmological spacetimes.