The Alcock Paczynski test with Baryon Acoustic Oscillations: systematic effects for future surveys

TL;DR

This paper assesses the systematic effects impacting the Alcock-Paczynski test using BAO features, emphasizing the roles of redshift space distortions and lensing corrections in future galaxy surveys.

Contribution

It provides a comprehensive formalism including relativistic effects to quantify systematic biases in the AP test with BAO, tailored for upcoming surveys like Euclid, DESI, and SKA.

Findings

Redshift space distortions cause up to 1% offsets in the AP test.

Lensing corrections affect amplitude but not shape, thus not systematic.

Redshift binning influences correlation measurements and peak positions.

Abstract

We investigate the Alcock Paczynski (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).