Combining probes of large-scale structure with COSMOLIKE

Developing accurate analysis techniques to combine various probes of cosmology is essential to tighten constraints on cosmological parameters and to check for inconsistencies in our model of the Universe. In this paper we develop a joint analysis framework for six different second-order statistics calculated from three tracers of the dark matter density field, namely galaxy position, shear, and magnification. We extend a data compression scheme developed in the context of shear-shear statistics (the so-called COSEBIs) to the other five second-order statistics, thereby significantly reducing the number of data points in the joint data vector. We use COSMOLIKE, a newly developed software framework for joint likelihood analyses, to forecast parameter constraints for the Dark Energy Survey. The simulated Monte Carlo Markov Chains cover a five-dimensional cosmological parameter space comparing the information content of the individual probes to several combined probes (CP) data vectors. Given the significant correlations of these second-order statistics we model all cross-terms in the covariance matrix; furthermore, we go beyond the Gaussian covariance approximation and use the halo model to include higher order correlations of the density field. We find that adding magnification information (including cross-probes with shear and clustering) noticeably increases the information content and that the correct modelling of the covariance (i.e. accounting for non-Gaussianity and cross-terms) is essential for accurate likelihood contours from the CP data vector. We also identify several null tests based on the degeneracy of magnification and shear statistics which can be used to quantify the contamination of data sets by astrophysical systematics and/or calibration issues.