# The Alcock Paczy'nski test with Baryon Acoustic Oscillations: systematic effects for future surveys

## Abstract

We investigate the Alcock Paczy'nski (AP) test applied to the Baryon Acoustic Oscillation (BAO) feature in the galaxy correlation function. By using a general formalism that includes relativistic effects, we quantify the importance of the linear redshift space distortions and gravitational lensing corrections to the galaxy number density fluctuation. We show that redshift space distortions significantly affect the shape of the correlation function, both in radial and transverse directions, causing different values of galaxy bias to induce offsets up to 1% in the AP test. On the other hand, we find that the lensing correction around the BAO scale modifies the amplitude but not the shape of the correlation function and therefore does not introduce any systematic effect. Furthermore, we investigate in details how the AP test is sensitive to redshift binning: a window function in transverse direction suppresses correlations and shifts the peak position toward smaller angular scales. We determine the correction that should be applied in order to account for this effect, when performing the test with data from three future planned galaxy redshift surveys: Euclid, the Dark Energy Spectroscopic Instrument (DESI) and the Square Kilometer Array (SKA).

- Authors:

- SISSA—International School for Advanced Studies, Via Bonomea 265, 34136 Trieste (Italy)
- INAF—Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, I-34143 Trieste (Italy)
- Université de Genève, Département de Physique Théorique and CAP, 24 quai Ernest-Ansermet, CH-1211 Genève 4 (Switzerland)

- Publication Date:

- OSTI Identifier:
- 22680031

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 02; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; AMPLITUDES; BARYONS; CORRELATION FUNCTIONS; CORRELATIONS; DENSITY; FLUCTUATIONS; GALAXIES; GRAVITATIONAL LENSES; NONLUMINOUS MATTER; OSCILLATIONS; RED SHIFT; RELATIVISTIC RANGE; SPACE

### Citation Formats

```
Lepori, Francesca, Viel, Matteo, Baccigalupi, Carlo, Dio, Enea Di, and Durrer, Ruth, E-mail: flepori@sissa.it, E-mail: enea.didio@oats.inaf.it, E-mail: viel@oats.inaf.it, E-mail: carlo.baccigalupi@sissa.it, E-mail: Ruth.Durrer@unige.ch.
```*The Alcock Paczy'nski test with Baryon Acoustic Oscillations: systematic effects for future surveys*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/02/020.

```
Lepori, Francesca, Viel, Matteo, Baccigalupi, Carlo, Dio, Enea Di, & Durrer, Ruth, E-mail: flepori@sissa.it, E-mail: enea.didio@oats.inaf.it, E-mail: viel@oats.inaf.it, E-mail: carlo.baccigalupi@sissa.it, E-mail: Ruth.Durrer@unige.ch.
```*The Alcock Paczy'nski test with Baryon Acoustic Oscillations: systematic effects for future surveys*. United States. doi:10.1088/1475-7516/2017/02/020.

```
Lepori, Francesca, Viel, Matteo, Baccigalupi, Carlo, Dio, Enea Di, and Durrer, Ruth, E-mail: flepori@sissa.it, E-mail: enea.didio@oats.inaf.it, E-mail: viel@oats.inaf.it, E-mail: carlo.baccigalupi@sissa.it, E-mail: Ruth.Durrer@unige.ch. Wed .
"The Alcock Paczy'nski test with Baryon Acoustic Oscillations: systematic effects for future surveys". United States.
doi:10.1088/1475-7516/2017/02/020.
```

```
@article{osti_22680031,
```

title = {The Alcock Paczy'nski test with Baryon Acoustic Oscillations: systematic effects for future surveys},

author = {Lepori, Francesca and Viel, Matteo and Baccigalupi, Carlo and Dio, Enea Di and Durrer, Ruth, E-mail: flepori@sissa.it, E-mail: enea.didio@oats.inaf.it, E-mail: viel@oats.inaf.it, E-mail: carlo.baccigalupi@sissa.it, E-mail: Ruth.Durrer@unige.ch},

abstractNote = {We investigate the Alcock Paczy'nski (AP) test applied to the Baryon Acoustic Oscillation (BAO) feature in the galaxy correlation function. By using a general formalism that includes relativistic effects, we quantify the importance of the linear redshift space distortions and gravitational lensing corrections to the galaxy number density fluctuation. We show that redshift space distortions significantly affect the shape of the correlation function, both in radial and transverse directions, causing different values of galaxy bias to induce offsets up to 1% in the AP test. On the other hand, we find that the lensing correction around the BAO scale modifies the amplitude but not the shape of the correlation function and therefore does not introduce any systematic effect. Furthermore, we investigate in details how the AP test is sensitive to redshift binning: a window function in transverse direction suppresses correlations and shifts the peak position toward smaller angular scales. We determine the correction that should be applied in order to account for this effect, when performing the test with data from three future planned galaxy redshift surveys: Euclid, the Dark Energy Spectroscopic Instrument (DESI) and the Square Kilometer Array (SKA).},

doi = {10.1088/1475-7516/2017/02/020},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 02,

volume = 2017,

place = {United States},

year = {Wed Feb 01 00:00:00 EST 2017},

month = {Wed Feb 01 00:00:00 EST 2017}

}