Double Soft Limits of Cosmological Correlations

TL;DR

This paper derives and verifies identities relating long- and short-wavelength cosmological correlation functions using symmetry principles and the background wave method, extending Weinberg's adiabatic modes.

Contribution

It introduces a unique extension of Weinberg's adiabatic modes to derive soft identities for cosmological correlations.

Findings

Correlation functions with long and short modes are related through derived identities.

The identities are verified through multiple consistency checks.

The extension of adiabatic modes is shown to be unique.

Abstract

Correlation functions of two long-wavelength modes with several short-wavelength modes are shown to be related to lower order correlation functions, using the background wave method, and independently, by exploiting symmetries of the wavefunction of the Universe. These soft identities follow from the non-linear extension of the adiabatic modes of Weinberg, and their generalization by Hinterbichler et. al. The extension is shown to be unique. A few checks of the identities are presented.