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

TL;DR

This paper introduces a new method to directly reconstruct the dark matter correlation function by combining galaxy clustering and galaxy-galaxy lensing data, improving accuracy on small scales and aiding cosmological model discrimination.

Contribution

The study develops a novel statistic that suppresses small-scale contributions, enabling accurate estimation of the dark matter correlation function from observational data.

Findings

The new statistic achieves a few percent accuracy in the correlation coefficient down to 5 Mpc/h.

The residual incoherence is well explained by a scale-dependent bias model.

The method can distinguish between different cosmological models effectively.

Abstract

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 this study we develop 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. 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 pre-existing 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 5 Mpc/h. Furthermore, the residual incoherence between the galaxy and matter fields can be explained using a theoretical model for scale-dependent bias, giving us a final estimator that is unbiased to within 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 show the viability of our new statistic to distinguish between cosmological models.