Combining Probes of Large-Scale Structure
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 of 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 simulate a likelihood analysis for the Dark Energy Survey (DES) in a five dimensional cosmological parameter space (plus basic parametrization for bias and correlation parameter) 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 modeling both, Non-Gaussianity and cross terms, is essential for accurate likelihood contours from the CP data vector; assuming Gaussian errors or uncorrelated probes impacts the contours at a similar level as assuming perfect knowledge of galaxy bias. We also identify several nulltests 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.