Cosmological Constraints from a Combination of Galaxy Clustering & Lensing -- II. Fisher Matrix Analysis

TL;DR

This paper uses a Fisher matrix analysis combining galaxy clustering, lensing, and abundance data to tightly constrain key cosmological parameters, accounting for galaxy bias uncertainties.

Contribution

It introduces a joint analysis framework that integrates galaxy observables with halo occupation modeling to improve cosmological parameter constraints.

Findings

Joint analysis yields tight, nearly uncorrelated constraints on cosmological parameters.

Constraints are competitive with other methods like cluster counts and BAO.

Method effectively marginalizes over galaxy bias uncertainties.

Abstract

We quantify the accuracy with which the cosmological parameters characterizing the energy density of matter (\Omega_m), the amplitude of the power spectrum of matter fluctuations (\sigma_8), the energy density of neutrinos (\Omega_{\nu}) and the dark energy equation of state (w_0) can be constrained using data from large galaxy redshift surveys. We advocate a joint analysis of the abundance of galaxies, galaxy clustering, and the galaxy-galaxy weak lensing signal in order to simultaneously constrain the halo occupation statistics (i.e., galaxy bias) and the cosmological parameters of interest. We parameterize the halo occupation distribution of galaxies in terms of the conditional luminosity function and use the analytical framework of the halo model described in our companion paper (van den Bosch et al. 2012), to predict the relevant observables. By performing a Fisher matrix analysis, we show that a joint analysis of these observables, even with the precision with which they are currently measured from the Sloan Digital Sky Survey, can be used to obtain tight constraints on the cosmological parameters, fully marginalized over uncertainties in galaxy bias. We demonstrate that the cosmological constraints from such an analysis are nearly uncorrelated with the halo occupation distribution constraints, thus, minimizing the systematic impact of any imperfections in modeling the halo occupation statistics on the cosmological constraints. In fact, we demonstrate that the constraints from such an analysis are both complementary to and competitive with existing constraints on these parameters from a number of other techniques, such as cluster abundances, cosmic shear and/or baryon acoustic oscillations, thus paving the way to test the concordance cosmological model.