Principal Component Analysis of Weak Lensing Surveys

Aims. We study degeneracies between cosmological parameters and measurement errors from cosmic shear surveys. We simulate realistic survey topologies with non-uniform sky coverage, and quantify the effect of survey geometry, depth and noise from intrinsic galaxy ellipticities on the parameter errors. This analysis allows us to optimise the survey geometry. Methods. We carry out a principal component analysis of the Fisher information matrix to assess the accuracy with which linear combinations of parameters can be determined. Using the shear two-point correlation functions and the aperture mass dispersion, which can directly be measured from the shear maps, we study various degeneracy directions in a multi-dimensional parameter space spanned by Ωm, ΩΛ, σ8, the shape parameter Γ, the spectral index ns, along with parameters that specify the distribution of source galaxies. Results. A principal component analysis is an effective tool to probe the extent and dimensionality of the error ellipsoid. If only three parameters are to be obtained from weak lensing data, a single principal component is dominant and contains all information about the main parameter degeneracies and their errors. For four or more free parameters, the first two principal components dominate the parameter errors. The degeneracy directions are insensitive against variations in the noise or survey geometry. The variance of the dominant principal component of the Fisher matrix, however, scales with the noise. Further, it shows a minimum for survey strategies which have small cosmic variance and measure the shear correlation up to several degrees. This minimum is less pronounced if external priors are added, rendering the optimisation less effective. The minimisation of the Fisher error ellipsoid can lead to slightly different results than the principal component analysis.