Algorithm for the direct reconstruction of the dark matter correlation function from weak lensing and galaxy clustering

The clustering of matter on cosmological scales is an essential probe for studying the physical origin and composition of our Universe. To date, most of the direct studies have focused on shear-shear weak lensing correlations, but it is also possible to extract the dark matter clustering by combining galaxy-clustering and galaxy-galaxy-lensing measurements. In order to extract the required information, one must relate the observable galaxy distribution to the underlying dark matter distribution. In this study we develop in detail a method that can constrain the dark matter correlation function from galaxy clustering and galaxy-galaxy-lensing measurements, by focusing on the correlation coefficient between the galaxy and matter overdensity fields. Our goal is to develop an estimator that maximally correlates the two. To generate a mock galaxy catalogue for testing purposes, we use the halo occupation distribution approach applied to a large ensemble of N-body simulations to model preexisting SDSS luminous red galaxy sample observations. Using this mock catalogue, we show that a direct comparison between the excess surface mass density measured by lensing and its corresponding galaxy clustering quantity is not optimal. We develop a new statistic that suppresses the small-scale contributions to these observations and show that this new statistic leads to a cross-correlation coefficient that is within a few percent of unity down to 5h(-1) Mpc. Furthermore, the residual incoherence between the galaxy and matter fields can be explained using a theoretical model for scale-dependent galaxy bias, giving us a final estimator that is unbiased to within 1%, so that we can reconstruct the dark matter clustering power spectrum at this accuracy up to k similar to 1h Mpc(-1). We also perform a comprehensive study of other physical effects that can affect the analysis, such as redshift space distortions and differences in radial windows between galaxy clustering and weak lensing observations. We apply the method to a range of cosmological models and explicitly show the viability of our new statistic to distinguish between cosmological models.