Optimal polarisation equations in FLRW universes

TL;DR

This paper derives a unified approach to compute photon polarisation modes in various FLRW cosmologies, simplifying the hierarchy needed for scalar, vector, and tensor perturbations across different curvature models.

Contribution

It introduces a single hierarchy method to calculate E- and B-mode polarisation for all perturbation types in flat, open, and closed FLRW universes, extending previous work.

Findings

Unified hierarchy for polarisation modes across all perturbation types

Applicable to flat, open, and closed FLRW cosmologies

Simplifies calculations of photon polarisation in cosmological models

Abstract

This paper presents the linearised Boltzmann equation for photons for scalar, vector and tensor perturbations in flat, open and closed FLRW cosmologies. We show that E- and B-mode polarisation for all types can be computed using only a single hierarchy. This was previously shown explicitly for tensor modes in flat cosmologies but not for vectors, and not for non-flat cosmologies.