# Beyond the plane-parallel approximation for redshift surveys

## Abstract

Redshift -space distortions privilege the location of the observer in cosmological redshift surveys, breaking the translational symmetry of the underlying theory. This violation of statistical homogeneity has consequences for the modelling of clustering observables, leading to what are frequently called 'wide-angle effects'. We study these effects analytically, computing their signature in the clustering of the multipoles in configuration and Fourier space. We take into account both physical wide-angle contributions as well as the terms generated by the galaxy selection function. Similar considerations also affect the way power spectrum estimators are constructed. We quantify in an analytical way the biases that enter and clarify the relation between what we measure and the underlying theoretical modelling. The presence of an angular window function is also discussed. Motivated by this analysis, we present new estimators for the three dimensional Cartesian power spectrum and bispectrum multipoles written in terms of spherical Fourier-Bessel coefficients. In conclusion, we show how the latter have several interesting properties, allowing in particular a clear separation between angular and radial modes.

- Authors:

- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1461164

- Grant/Contract Number:
- AC02-05CH11231

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Monthly Notices of the Royal Astronomical Society

- Additional Journal Information:
- Journal Volume: 476; Journal Issue: 4; Related Information: © 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society.; Journal ID: ISSN 0035-8711

- Publisher:
- Royal Astronomical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; methods: analytical; methods: observational; cosmological parameters; large-scale structure of Universe; cosmology: theory

### Citation Formats

```
Castorina, Emanuele, and White, Martin. Beyond the plane-parallel approximation for redshift surveys. United States: N. p., 2018.
Web. doi:10.1093/mnras/sty410.
```

```
Castorina, Emanuele, & White, Martin. Beyond the plane-parallel approximation for redshift surveys. United States. doi:10.1093/mnras/sty410.
```

```
Castorina, Emanuele, and White, Martin. Mon .
"Beyond the plane-parallel approximation for redshift surveys". United States. doi:10.1093/mnras/sty410. https://www.osti.gov/servlets/purl/1461164.
```

```
@article{osti_1461164,
```

title = {Beyond the plane-parallel approximation for redshift surveys},

author = {Castorina, Emanuele and White, Martin},

abstractNote = {Redshift -space distortions privilege the location of the observer in cosmological redshift surveys, breaking the translational symmetry of the underlying theory. This violation of statistical homogeneity has consequences for the modelling of clustering observables, leading to what are frequently called 'wide-angle effects'. We study these effects analytically, computing their signature in the clustering of the multipoles in configuration and Fourier space. We take into account both physical wide-angle contributions as well as the terms generated by the galaxy selection function. Similar considerations also affect the way power spectrum estimators are constructed. We quantify in an analytical way the biases that enter and clarify the relation between what we measure and the underlying theoretical modelling. The presence of an angular window function is also discussed. Motivated by this analysis, we present new estimators for the three dimensional Cartesian power spectrum and bispectrum multipoles written in terms of spherical Fourier-Bessel coefficients. In conclusion, we show how the latter have several interesting properties, allowing in particular a clear separation between angular and radial modes.},

doi = {10.1093/mnras/sty410},

journal = {Monthly Notices of the Royal Astronomical Society},

number = 4,

volume = 476,

place = {United States},

year = {2018},

month = {2}

}

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