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