# Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter

## Abstract

We develop a perturbative approach to redshift space distortions (RSD) using the phase space distribution function approach and apply it to the dark matter redshift space power spectrum and its moments. RSD can be written as a sum over density weighted velocity moments correlators, with the lowest order being density, momentum density and stress energy density. We use standard and extended perturbation theory (PT) to determine their auto and cross correlators, comparing them to N-body simulations. We show which of the terms can be modeled well with the standard PT and which need additional terms that include higher order corrections which cannot be modeled in PT. Most of these additional terms are related to the small scale velocity dispersion effects, the so called finger of god (FoG) effects, which affect some, but not all, of the terms in this expansion, and which can be approximately modeled using a simple physically motivated ansatz such as the halo model. We point out that there are several velocity dispersions that enter into the detailed RSD analysis with very different amplitudes, which can be approximately predicted by the halo model. In contrast to previous models our approach systematically includes all of the terms atmore »

- Authors:

- Institute for Theoretical Physics, University of Zürich, Winterthurerstrasse 190, 8057 Zürich (Switzerland)
- Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720 (United States)
- Institute for the Early Universe, Ewha Womans University, Seoul 120-750, S. Korea (Korea, Republic of)

- Publication Date:

- OSTI Identifier:
- 22279678

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2012; Journal Issue: 11; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; AMPLITUDES; APPROXIMATIONS; ASTROPHYSICS; COMPARATIVE EVALUATIONS; CORRECTIONS; COSMOLOGY; DISTRIBUTION FUNCTIONS; ENERGY DENSITY; ENERGY SPECTRA; NONLUMINOUS MATTER; PERTURBATION THEORY; PHASE SPACE; RED SHIFT

### Citation Formats

```
Vlah, Zvonimir, Seljak, Uroš, Baldauf, Tobias, McDonald, Patrick, and Okumura, Teppei, E-mail: zvlah@physik.uzh.ch, E-mail: seljak@physik.uzh.ch, E-mail: pvmcdonald@lbl.gov, E-mail: teppei@ewha.ac.kr, E-mail: baldauf@physik.uzh.ch.
```*Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter*. United States: N. p., 2012.
Web. doi:10.1088/1475-7516/2012/11/009.

```
Vlah, Zvonimir, Seljak, Uroš, Baldauf, Tobias, McDonald, Patrick, & Okumura, Teppei, E-mail: zvlah@physik.uzh.ch, E-mail: seljak@physik.uzh.ch, E-mail: pvmcdonald@lbl.gov, E-mail: teppei@ewha.ac.kr, E-mail: baldauf@physik.uzh.ch.
```*Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter*. United States. doi:10.1088/1475-7516/2012/11/009.

```
Vlah, Zvonimir, Seljak, Uroš, Baldauf, Tobias, McDonald, Patrick, and Okumura, Teppei, E-mail: zvlah@physik.uzh.ch, E-mail: seljak@physik.uzh.ch, E-mail: pvmcdonald@lbl.gov, E-mail: teppei@ewha.ac.kr, E-mail: baldauf@physik.uzh.ch. Thu .
"Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter". United States. doi:10.1088/1475-7516/2012/11/009.
```

```
@article{osti_22279678,
```

title = {Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter},

author = {Vlah, Zvonimir and Seljak, Uroš and Baldauf, Tobias and McDonald, Patrick and Okumura, Teppei, E-mail: zvlah@physik.uzh.ch, E-mail: seljak@physik.uzh.ch, E-mail: pvmcdonald@lbl.gov, E-mail: teppei@ewha.ac.kr, E-mail: baldauf@physik.uzh.ch},

abstractNote = {We develop a perturbative approach to redshift space distortions (RSD) using the phase space distribution function approach and apply it to the dark matter redshift space power spectrum and its moments. RSD can be written as a sum over density weighted velocity moments correlators, with the lowest order being density, momentum density and stress energy density. We use standard and extended perturbation theory (PT) to determine their auto and cross correlators, comparing them to N-body simulations. We show which of the terms can be modeled well with the standard PT and which need additional terms that include higher order corrections which cannot be modeled in PT. Most of these additional terms are related to the small scale velocity dispersion effects, the so called finger of god (FoG) effects, which affect some, but not all, of the terms in this expansion, and which can be approximately modeled using a simple physically motivated ansatz such as the halo model. We point out that there are several velocity dispersions that enter into the detailed RSD analysis with very different amplitudes, which can be approximately predicted by the halo model. In contrast to previous models our approach systematically includes all of the terms at a given order in PT and provides a physical interpretation for the small scale dispersion values. We investigate RSD power spectrum as a function of μ, the cosine of the angle between the Fourier mode and line of sight, focusing on the lowest order powers of μ and multipole moments which dominate the observable RSD power spectrum. Overall we find considerable success in modeling many, but not all, of the terms in this expansion. This is similar to the situation in real space, but predicting power spectrum in redshift space is more difficult because of the explicit influence of small scale dispersion type effects in RSD, which extend to very large scales.},

doi = {10.1088/1475-7516/2012/11/009},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 11,

volume = 2012,

place = {United States},

year = {2012},

month = {11}

}