Cosmological Parameters from Second- and Third-Order Cosmic Shear Statistics

Abstract

The weak gravitational lensing effect caused by the large-scale structure of the matter in the Universe (cosmic shear) is a powerful tool to study the matter distribution on very large scales. Cosmic shear surveys provide high-precision measurements of the large-scale distribution of matter in the Universe and yield valuable information about cosmology. In this thesis I study the efficacy of cosmic shear statistics to constrain cosmological parameters. <br /> In the first part of this work, different strategies of shear surveys are considered and their influence on the measurement accuracy of cosmological parameters is investigated. From Monte-Carlo simulations, the covariance of second-order shear statistics, in particular the aperture mass dispersion <<i>M</i>_ap²>, is obtained. The covariance encodes the measurement errors and correlations between different angular scales which depend on the survey design. Using the Fisher information matrix, Karhunen-Loève eigenmodes and likelihood techniques, various survey settings are compared with the result that a rigorous sampling on medium and large angular scales is more important than a small cosmic variance. By appropriately choosing the survey geometry a 25 percent improvement on the 1s-errors on cosmological parameters is possible. <br /> The second part of this thesis presents predictions of the improvement of constraints on cosmological parameters by combining second- and third-order aperture mass statistics of cosmic shear. The three-point correlation function and the third-order aperture mass statistics are calculated from theoretical non-linear models of structure formation. These predictions are tested and compared with ray-tracing simulations. The dependence of the third-order aperture mass statistics with respect to cosmological parameters is discussed and a two-dimensional visualization of the shear three-point correlation function is presented. After this preparatory work, the second- and third-order aperture mass statistics, <<i>M</i>_ap²> and <<i>M</i>_ap³>, are combined to reduce near-degeneracies between cosmological parameters and to improve the resulting error bars. From ?CDM ray-tracing simulations, the covariance and the cross-correlation of <<i>M</i>_ap²> and <<i>M</i>_ap³> are estimated. A Fisher matrix analysis shows that the combination of second- and third-order statistics can partially lift the parameter degeneracies, e.g. between Ω_m and σ₈. The resulting error bars on all considered cosmological parameters are reduced by a factor of 10.