Statistical challenges in weak lensing cosmology

TL;DR

This paper investigates the statistical limits of extracting initial Gaussian information from weak lensing data, emphasizing the impact of super-sample variance on the information content of power spectrum and bispectrum measurements.

Contribution

It provides a detailed analysis of super-sample variance effects on weak lensing correlations and assesses the information content of two- and three-point statistics in cosmological surveys.

Findings

Super-sample variance significantly affects weak lensing correlation measurements.

Correlations between different multipoles and triangle configurations are crucial for accurate analysis.

The information content in weak lensing observables is limited by super-sample variance.

Abstract

Cosmological weak lensing is the powerful probe of cosmology. Here we address one of the most fundamental, statistical questions inherent in weak lensing cosmology: whether or not we can recover the initial Gaussian information content of large-scale structure by combining the weak lensing observables, here focused on the weak lensing power spectrum and bispectrum. To address this question we fully take into account correlations between the power spectra of different multipoles and the bispectra of different triangle configurations, measured from a finite area survey. In particular we show that super-survey modes whose length scale is larger than or comparable with the survey size cause significant sample variance in the weak lensing correlations via the mode-coupling with sub-survey modes due to nonlinear gravitational clustering -- the so-called super-sample variance. In this paper we discuss the origin of the super-sample variance and then study the information content inherent in the weak lensing correlation functions up to three-point level.