Cosmological constraints from a combination of galaxy clustering and lensing - I. Theoretical framework

• Published in: Monthly notices of the Royal Astronomical Society Vol. 430; no. 2; pp. 725 - 746
• Main Authors: van den Bosch, Frank C., More, Surhud, Cacciato, Marcello, Mo, Houjun, Yang, Xiaohu
• Format: Journal Article
• Language: English
• Published: London Oxford University Press 01-04-2013
• Subjects: Correlation analysis; Cosmology; Luminosity; Star & galaxy formation; methods: statistical; cosmological parameters; dark matter; large-scale structure of Universe; galaxies: haloes
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/sts006

We present a new method that simultaneously solves for cosmology and galaxy bias on non-linear scales. The method uses the halo model to analytically describe the (non-linear) matter distribution, and the conditional luminosity function (CLF) to specify the halo occupation statistics. For a given choice of cosmological parameters, this model can be used to predict the galaxy luminosity function, as well as the two-point correlation functions of galaxies, and the galaxy-galaxy lensing signal, both as a function of scale and luminosity. These observables have been reliably measured from the Sloan Digital Sky Survey. In this paper, the first in a series, we present the detailed, analytical model, which we test against mock galaxy redshift surveys constructed from high-resolution numerical N-body simulations. We demonstrate that our model, which includes scale dependence of the halo bias and a proper treatment of halo exclusion, reproduces the three-dimensional galaxy-galaxy correlation and the galaxy-matter cross-correlation (which can be projected to predict the observables) with an accuracy better than 10 (in most cases 5) per cent. Ignoring either of these effects, as is often done, results in systematic errors that easily exceed 40 per cent on scales of ∼ 1 h
− 1 Mpc, where the data are typically most accurate. Finally, since the projected correlation functions of galaxies are never obtained by integrating the redshift-space correlation function along the line of sight out to infinity, simply because the data only cover a finite volume, they are still affected by residual redshift-space distortions (RRSDs). Ignoring these, as done in numerous studies in the past, results in systematic errors that easily exceed 20 per cent on large scales (r
p 10 h
− 1 Mpc). We show that it is fairly straightforward to correct for these RRSDs, to an accuracy better than ∼ 2 per cent, using a mildly modified version of the linear Kaiser formalism.