Modelling the angular correlation function and its full covariance in photometric galaxy surveys

Near-future cosmology will see the advent of wide-area photometric galaxy surveys, such as the Dark Energy Survey (DES), that extend to high redshifts (z similar to 1-2) but give poor radial distance resolution. In such cases splitting the data into redshift bins and using the angular correlation function w(theta), or the C-l power spectrum, will become the standard approach to extracting cosmological information or to studying the nature of dark energy through the baryon acoustic oscillations (BAO) probe. In this work we present a detailed model for w(theta) at large scales as a function of redshift and binwidth, including all relevant effects, namely non-linear gravitational clustering, bias, redshift space distortions and photo-z uncertainties. We also present a model for the full covariance matrix, characterizing the angular correlation measurements, that takes into account the same effects as for w(theta) and also the possibility of a shot-noise component and partial sky coverage. Provided with a large-volume N-body simulation from the MICE collaboration, we built several ensembles of mock redshift bins with a sky coverage and depth typical of forthcoming photometric surveys. The model for the angular correlation and the one for the covariance matrix agree remarkably well with the mock measurements in all configurations. The prospects for a full shape analysis of w(theta) at BAO scales in forthcoming photometric surveys such as DES are thus very encouraging.