Cosmological parameters from combined second- and third-order aperture mass statistics of cosmic shear

Institut f. Astrophysik u. Extraterrestrische Forschung, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany e-mail: kilbinge@astro.uni-bonn.de

Received: 29 May 2005
Accepted: 4 July 2005

Abstract

We present predictions for cosmological parameter constraints from combined measurements of second- and third-order statistics of cosmic shear. We define the generalized third-order aperture mass statistics and show that it contains much more information about the bispectrum of the projected matter density than the skewness of the aperture mass. From theoretical models as well as from ΛCDM ray-tracing simulations, we calculate and and their dependence on cosmological parameters. The covariances including shot noise and cosmic variance of , and their cross-correlation are calculated using ray-tracing simulations. We perform an extensive Fisher matrix analysis, and for various combinations of cosmological parameters, we predict 1-σ-errors corresponding to measurements from a deep 29 square degree cosmic shear survey. Although the parameter degeneracies can not be lifted completely, the (linear) combination of second- and third-order aperture mass statistics reduces the errors significantly. The strong degeneracy between  and , present for all second-order cosmic shear measures, is diminished substantially, whereas less improvement is found for the near-degenerate pair consisting of the shape parameter Γ and the spectral index n_s. Uncertainties in the source galaxy redshift z₀ increase the errors of all other parameters.