Joint Analysis of Gravitational Lensing, Clustering and Abundance: Toward the Unification of Large-Scale Structure Analysis

Abstract

We explore three different methods based on weak lensing to extract cosmological constraints from the large-scale structure. In the first approach (method I), small-scale galaxy lensing measurements of their halo mass provide a constraint on the halo bias, which can be combined with the large-scale galaxy clustering to measure the dark matter clustering. In the second approach (method II), large-scale galaxy clustering and large-scale galaxy-galaxy lensing can be combined into a direct measurement of the dark matter clustering. These two methods can be combined into one method I+II to make use of lensing measurements on all scales. In the third approach (method III), we add abundance information to the method I. We explore the statistical power of these three approaches as a function of galaxy luminosity to investigate the optimal mass range for each method and their cosmological constraining power. In the case of the SDSS, we find that the three methods give comparable constraints, but not in the same mass range: the method II works best for halos of M~10^13 Msun, and the methods I and III work best for halos of M~10^14 Msun. We discuss the robustness of each method against various systematics. Furthermore, we extend the analysis to the future large-scale galaxy surveys and find that the cluster abundance method is not superior to the combined method I+II, both in terms of statistical power and robustness against systematic errors. The cosmic shear-shear correlation analysis in the future surveys yields constraints as strong as the combined method, but suffer from additional systematic effects. We thus advocate the combined analysis of clustering and lensing (method I+II) as a powerful alternative to other large-scale probes. Our analysis provides a guidance to observers planning large-scale galaxy surveys such as the DES, Euclid, and the LSST.