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

Free access article

Issue		A&A Volume 442, Number 1, October IV 2005


Page(s)		69 - 83
Section		Cosmology (including clusters of galaxies)
DOI		http://dx.doi.org/10.1051/0004-6361:20053531

A&A 442, 69-83 (2005)
DOI: 10.1051/0004-6361:20053531

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

M. Kilbinger and P. Schneider

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 $\langle M_{\rm ap}^3 \rangle$ 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 $\Lambda$ CDM ray-tracing simulations, we calculate $\langle M_{\rm ap}^2 \rangle$ and $\langle M_{\rm ap}^3 \rangle$ and their dependence on cosmological parameters. The covariances including shot noise and cosmic variance of $M_{\rm ap}^2$ , $M_{\rm ap}^3$ 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- $\sigma$ -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 $\Omega_{\rm m}$ and $\sigma_8$ , 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 $\Gamma$ and the spectral index $n_{\rm s}$ . Uncertainties in the source galaxy redshift z₀ increase the errors of all other parameters.

Key words: cosmology: large-scale structure of Universe -- gravitational lensing -- cosmology: cosmological parameters

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