Modeling the angular correlation function and its full covariance in Photometric Galaxy Surveys

TL;DR

This paper develops a comprehensive model for the angular correlation function and its covariance in photometric galaxy surveys, accounting for key effects and validated against simulations, enhancing future cosmological analyses.

Contribution

It introduces a detailed model for $w(\theta)$ and its covariance, including nonlinear, bias, redshift distortions, and photo-z uncertainties, validated with mock simulations for upcoming surveys.

Findings

Model agrees well with mock measurements across configurations.

Full covariance model captures shot noise and partial sky coverage effects.

Results support the feasibility of shape analysis at BAO scales in future surveys.

Abstract

Near future cosmology will see the advent of wide area photometric galaxy surveys, like the Dark Energy Survey (DES), that extent to high redshifts (z ~ 1 - 2) but with poor radial distance resolution. In such cases splitting the data into redshift bins and using the angular correlation function $w(\theta)$, or the $C_{\ell}$ power spectrum, will become the standard approach to extract cosmological information or to study 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 bin width, including all relevant effects, namely nonlinear 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.