Karhunen-Loeve Analysis for Weak Gravitational Lensing

TL;DR

This paper applies Karhunen-Loeve analysis to enhance the efficiency and accuracy of weak gravitational lensing data analysis, aiding in cosmological parameter estimation from large-scale surveys.

Contribution

It introduces novel applications of KL analysis to 3D mapping, shear peak statistics, and parameter estimation with gappy data in weak lensing studies.

Findings

Improved 3D tomographic mapping techniques.

Effective handling of incomplete shear data.

Enhanced parameter estimation accuracy.

Abstract

In the past decade, weak gravitational lensing has become an important tool in the study of the universe at the largest scale, giving insights into the distribution of dark matter, the expansion of the universe, and the nature of dark energy. This thesis research explores several applications of Karhunen-Loeve (KL) analysis to speed and improve the comparison of weak lensing shear catalogs to theory in order to constrain cosmological parameters in current and future lensing surveys. After providing a brief introduction to cosmology and to KL analysis, this work addresses three related aspects of weak lensing analysis: (1) Three-dimensional tomographic mapping (based on work published in Vanderplas et al. 2011); (2) Shear peak statistics with incomplete/gappy data (based on work published in Vanderplas et al. 2012); and (3) two-point parameter estimation from gappy data using KL modes (previously unpublished)... [this abstract has been abbreviated; please see the thesis for the full abstract].