A&A 482, 9-19 (2008)

DOI: 10.1051/0004-6361:20078573

## Comparing cosmic shear measures

##### Optimizing the information content of cosmic shear data vectors

**T. Eifler**

^{1}, M. Kilbinger^{1, 2}, and P. Schneider^{1}^{1}Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany

e-mail: tim.eifler@astro.uni-bonn.de

^{2}Institut d'Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France

(Received 29 August 2007 / Accepted 12 January 2008)

** Abstract ***Aims. *We introduce an optimized data vector of cosmic shear measures
. This data vector has high information content, is not sensitive to B-mode contamination, and only shows small correlation between data points of different angular scales.*Methods. *We show that a data vector of the two-point correlation function (2PCF), hereafter denoted as , in general contains more information on cosmological parameters compared to a data vector of the aperture mass dispersion, hereafter referred to as
. The reason for this is the fact that
lacks the information of the convergence power spectrum
on large angular scales, which is contained in . Nevertheless,
has valuable properties (small correlation between data points of different angular scales, not sensitive to B-mode contamination) that one wants to preserve in an optimized data vector. Therefore we combine and
to a new data vector
, which retains the advantages of
and is also sensitive to the large-scale information of
. We compare the information content of the three data vectors by performing a detailed likelihood analysis and use ray-tracing simulations to derive the covariance matrices. In the last part of the paper we contaminate all data vectors with B-modes on small angular scales and examine their robustness against this contamination.*Results. *The combined data vector
strongly improves constraints on cosmological parameters compared to
. Although, the information content of is higher in the case of a pure E-mode signal, in the more realistic case where B-modes are present the 2PCF data vector is strongly contaminated and yields biased cosmological parameter estimates. The new data vector
shows to be robust against this contamination. Furthermore the individual data points of
show a much smaller correlation compared to , leading to an almost diagonal covariance matrix.

**Key words:**cosmology: theory

**--**gravitational lensing

**--**large-scale structure of Universe

**--**methods: statistical

**©**

*ESO 2008*