Gauging the cosmic microwave background

TL;DR

This paper derives a new expression for CMB anisotropies, focusing on gauge issues and super-Hubble modes, showing that their contribution to the dipole is strongly suppressed, which clarifies previous conflicting claims.

Contribution

It provides an exact, perturbatively expandable expression for CMB anisotropies with a detailed analysis of super-Hubble mode effects and gauge considerations.

Findings

Super-Hubble adiabatic modes do not significantly contribute to the CMB dipole.

The derived transfer function accurately describes dipole behavior at long wavelengths.

The suppression of super-Hubble contributions is a geometric consequence of adiabaticity.

Abstract

We provide a new derivation of the anisotropies of the cosmic microwave background (CMB), and find an exact expression that can be readily expanded perturbatively. Close attention is paid to gauge issues, with the motivation to examine the effect of super-Hubble modes on the CMB. We calculate a transfer function that encodes the behaviour of the dipole, and examine its long-wavelength behaviour. We show that contributions to the dipole from adiabatic super-Hubble modes are strongly suppressed, even in the presence of a cosmological constant, contrary to claims in the literature. We also introduce a naturally defined CMB monopole, which exhibits closely analogous long-wavelength behaviour. We discuss the geometrical origin of this super-Hubble suppression, pointing out that it is a simple reflection of adiabaticity, and hence argue that it will occur regardless of the matter content.