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

## 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.

- Authors:

- Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX United Kingdom (United Kingdom)
- Department of Physics and Astronomy, University of Sussex, Pevensey II Building, Brighton, BN1 9QH United Kingdom (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22525875

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 04; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANISOTROPY; BOLTZMANN EQUATION; COSMOLOGY; DISTRIBUTION FUNCTIONS; NONLINEAR PROBLEMS; PERTURBATION THEORY; PHOTONS; POTENTIALS; QUANTUM OPERATORS; RECOMBINATION; RELICT RADIATION; S CODES

### Citation Formats

```
Fidler, Christian, Koyama, Kazuya, and Pettinari, Guido W., E-mail: christian.fidler@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk, E-mail: guido.pettinari@gmail.com.
```*A new line-of-sight approach to the non-linear Cosmic Microwave Background*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/04/037.

```
Fidler, Christian, Koyama, Kazuya, & Pettinari, Guido W., E-mail: christian.fidler@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk, E-mail: guido.pettinari@gmail.com.
```*A new line-of-sight approach to the non-linear Cosmic Microwave Background*. United States. doi:10.1088/1475-7516/2015/04/037.

```
Fidler, Christian, Koyama, Kazuya, and Pettinari, Guido W., E-mail: christian.fidler@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk, E-mail: guido.pettinari@gmail.com. Wed .
"A new line-of-sight approach to the non-linear Cosmic Microwave Background". United States.
doi:10.1088/1475-7516/2015/04/037.
```

```
@article{osti_22525875,
```

title = {A new line-of-sight approach to the non-linear Cosmic Microwave Background},

author = {Fidler, Christian and Koyama, Kazuya and Pettinari, Guido W., E-mail: christian.fidler@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk, E-mail: guido.pettinari@gmail.com},

abstractNote = {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.},

doi = {10.1088/1475-7516/2015/04/037},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 04,

volume = 2015,

place = {United States},

year = {Wed Apr 01 00:00:00 EDT 2015},

month = {Wed Apr 01 00:00:00 EDT 2015}

}