The Alcock-Paczyński effect from Lyman-α forest correlations: Analysis validation with synthetic data

The three-dimensional distribution of the Lyα forest has been extensively used to constrain cosmology through measurements of the baryon acoustic oscillations (BAO) scale. However, more cosmological information could be extracted from the full shapes of the Lyα forest correlations through the Alcock-Paczynski (AP) effect. In this work, we prepare for a cosmological analysis of the full shape of the Lyα forest correlations by studying synthetic data of the extended Baryon Oscillation Spectroscopic Survey (eBOSS). We use a set of one hundred eBOSS synthetic data sets in order to validate such an analysis. These mocks undergo the same analysis process as the real data. We perform a full-shape analysis on the mean of the correlation functions measured from the one hundred eBOSS realizations, and find that our model of the Lyα correlations performs well on current data sets. We show that we are able to obtain an unbiased full-shape measurement of D_M/D_H(z_eff), where D_M is the transverse comoving distance, D_H is the Hubble distance, and z_eff is the effective redshift of the measurement. We test the fit over a range of scales, and decide to use a minimum separation of r_min=25 h^-1 Mpc. We also study and discuss the impact of the main contaminants affecting Lyα forest correlations, and give recommendations on how to perform such analysis with real data. While the final eBOSS Lyα BAO analysis measured D_M/D_H(z_eff=2.33) with 4% statistical precision, a full-shape fit of the same correlations could provide a ~2% measurement.