Comparing cosmic shear measures - Optimizing the information content of cosmic shear data vectors

Aims. We introduce an optimized data vector of cosmic shear measures (N). 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 xi, in general contains more information on cosmological parameters compared to a data vector of the aperture mass dispersion, hereafter referred to as < M-ap(2)>. The reason for this is the fact that < M-ap(2)> lacks the information of the convergence power spectrum (P-k) on large angular scales, which is contained xi. Nevertheless, < M-ap(2)> 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 xi and < M-ap(2)> to a new data vector N = (< M-ap(2)>(theta(1)),...,< M-ap(2)>(theta(n)),xi+(theta(0)), which retains the advantages of < M-ap(2)> and is also sensitive to the large-scale information of P-k. 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 N strongly improves constraints on cosmological parameters compared to < M-ap(2)>. Although, the information content of xi 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 N shows to be robust against this contamination. Furthermore the individual data points of N show a much smaller correlation compared to xi, leading to an almost diagonal covariance matrix.