Systematics of Adiabatic Modes: Flat Universes

TL;DR

This work systematically derives cosmological adiabatic modes for spatially-flat FLRW spacetimes with a single fluid, using Newtonian and comoving gauges and a gradient-expansion approach. It reproduces known modes and reveals new ones, including a vector adiabatic mode, a time-dependent scalar curvature mode for generic fluids, and a time-dependent tensor mode that arises when mixed with other perturbations; it also clarifies the classical versus quantum nature of adiabatic modes and analyzes Weinberg's second adiabatic mode in the finite-momentum limit. The paper provides preliminary soft-theorem discussions for the new vector and tensor modes and discusses implications for contracting universes and alternatives to inflation. Collectively, these results deepen the infrared structure of cosmological perturbations and offer model-independent constraints on correlators across different cosmic backgrounds.

Abstract

Adiabatic modes are cosmological perturbations that are locally indistinguishable from a (large) change of coordinates. At the classical level, they provide model independent solutions. At the quantum level, they lead to soft theorems for cosmological correlators. We present a systematic derivation of adiabatic modes in spatially-flat cosmological backgrounds with asymptotically-perfect fluids. We find several new adiabatic modes including vector, time-dependent tensor and time-dependent scalar modes. The new vector and tensor modes decay with time in standard cosmologies but are the leading modes in contracting universes. We present a preliminary derivation of the related soft theorems. In passing, we discuss a distinction between classical and quantum adiabatic modes, we clarify the subtle nature of Weinberg second adiabatic mode and point out that the adiabatic nature of a perturbation is a gauge dependent statement.