A new line-of-sight approach to the non-linear Cosmic Microwave Background

TL;DR

This paper introduces a transport operator formalism for line-of-sight integration to accurately compute CMB anisotropies at both linear and non-linear levels, enabling a comprehensive treatment of all physical effects in the Boltzmann equation.

Contribution

It presents a novel formalism that separates perturbative and non-perturbative effects, allowing integration with existing Boltzmann codes for higher-order CMB anisotropy calculations.

Findings

Framework can incorporate non-linear Newtonian potentials.

Allows combining standard remapping with Boltzmann codes at any perturbation order.

Provides a unified approach to compute all effects in the Boltzmann equation.

Abstract

We develop the transport operator formalism, a new line-of-sight integration framework to calculate the anisotropies of the Cosmic Microwave Background (CMB) at the linear and non-linear level. This formalism utilises a transformation operator that removes all inhomogeneous propagation effects acting on the photon distribution function, thus achieving a split between perturbative collisional effects at recombination and non-perturbative line-of-sight effects at later times. The former can be computed in the framework of standard cosmological perturbation theory with a second-order Boltzmann code such as SONG, while the latter can be treated within a separate perturbative scheme allowing the use of non-linear Newtonian potentials. We thus provide a consistent framework to compute all physical effects contained in the Boltzmann equation and to combine the standard remapping approach with Boltzmann codes at any order in perturbation theory, without assuming that all sources are localised at recombination.