Enabling the Weak Lensing Science in the 2020s

The 2020s are an exhilarating era for modern cosmology, particularly in the field of weak gravitational lensing science. With the completion of Stage-III imaging surveys such as the Dark Energy Survey (DES), the Subaru Hyper Suprime-Cam (HSC), and the Kilo-Degree Survey (KiDS) in the first half of the decade, weak lensing science has entered the realm of precision observation. These surveys have enabled us to meticulously observe the positions and shapes of hundreds of millions of galaxies, enabling weak gravitational lensing observation with high significance. Combined with other probes such as the cosmic microwave background (CMB), weak lensing allow us to test the standard Λ-CDM model for the universe. 

In the latter half of the decade, various survey telescopes, both ground-based like the Vera Rubin Observatory and space-based like the Roman Space Telescope, will become operational. These telescopes will provide datasets with larger coverage areas, deeper optical depths, and higher resolutions. Leveraging the statistical power of these telescopes, we can theoretically achieve higher precision in constraining the large-scale structure and dark energy, thus offering a stress testing to the Λ-CDM model. By measuring the large-scale structure at different redshifts, we can distinguish between models with different parameters w0 for the dark energy equation of state, including Λ-CDM, which assumes w₀ = −1, i.e., a constant dark energy density. These scientific objectives drive the current weak lensing observations and have the potential to reshape modern cosmology. 

However, the success of the Stage-IV imaging survey crucially relies on effectively addressing systematic errors in observation and analysis. As the statistical uncertainty decreases with the data volume of these surveys, the tolerance for systematic errors diminishes as well. All sources of systematic uncertainty increase in importance, and even those previously considered subdominant now attain statistical significance. Weak lensing encompasses a wide range of systematic sources, including astrophysical and observational systematics, and systematic effects introduced by analysis and modeling methods. 

This thesis will specifically address two of the aforementioned systematics. The first focus is on the systematics arising from the Point Spread Function (PSF). The PSF represents the probability distribution that characterizes the response of an imaging system to a point source in the observed sky scene. Accurate modeling and correction of the PSF are essential in weak lensing observations. While the influence of the second moments of the PSF on weak lensing shear is widely recognized, research on the impact of higher moments of the PSF remains limited. My study initiates and expands the investigation of weak lensing systematics stemming from the higher moments of the PSF. I developed a software suite called PSFHOME, which encompasses image simulation, error propagation, and modeling with regard to the PSF higher moments. Combining with real data from the Hyper-Suprime Cam (HSC), I study the multiplicative and additive bias induced by the PSF higher moments, as well as modeling and propagating such error to the downstream cosmological probes. Based on this understanding, I further proposed a methodological framework to detect, model, and mitigate the contamination of higher moments on the shear two-point correlation function ξ±. This framework is applied to investigate the Year-3 shear catalog from the HSC. Using this new framework, I show that previously unidentified systematic biases in weak lensing shear arising from the PSF fourth moments can be effectively modeled and mitigated. 

The second topic of focus in this study revolves around systematic errors associated with photometric redshift estimation, commonly referred to as photo-z. To achieve reliable constraints on cosmological parameters in weak lensing shear analyses, it is essential to effectively and accurately marginalize the nuisance parameters of the redshift distribution n(z) of the observed sample. I propose a Bayesian statistical approach, called Bayesian resampling, to fully marginalize the redshift uncertainty in the shear catalog during cosmic shear analysis. This method is compared to existing approaches described in the literature, specifically in the context of a mock cosmic shear analysis for the HSC Year-3 shear catalog. The comparison demonstrates that the new method and the existing approaches yield statistically consistent error bars for the cosmological parameter constraints in the HSC three-year analysis. But the difference will increase for future surveys.