# Making the leap I: Modelling the reconstructed lensing convergence PDF from cosmic shear with survey masks and systematics

**Authors:** Alexandre Barthelemy, Anik Halder, Zhengyangguang Gong, Cora Uhlemann  
**arXiv:** [2307.09468](https://arxiv.org/abs/2307.09468)  
**Date:** 2023-07-18  
**Summary page:** https://www.summarizepaper.com/en/paper/2307.09468v1/

## Key points

- Significant progress in developing a theoretical framework for studying cosmic large-scale structure statistics, focusing on weak-lensing one-point statistics in the mildly non-linear regime
- Theory of Large Deviations (LDT) shows promise in modeling various aspects of cosmic large-scale structure
- Objective is to bridge the gap between theory and practical data analysis using LDT
- Paper I demonstrates accurate modeling of Probability Distribution Function (PDF) of a reconstructed Kaiser-Squires convergence field under realistic conditions like those in Dark Energy Survey (DES)
- Addressing weak lensing systematics and higher-order lensing corrections due to intrinsic alignments, shear biases, photo-z errors, and baryonic feedback within their modeling approach
- Paper II will focus on validating robustness of modeling through simulated likelihood analyses before applying it to actual observational data
- Base model for true but observationally inaccessible convergence PDF from LDT detailed, along with Kaiser-Squires reconstruction procedure for κ field from a simulated full-sky shear field with a realistic mask
- Modifications made to adapt original LDT theoretical model to account for reconstruction process tested against N-body simulations
- Strategies presented for incorporating higher-order lensing effects and addressing astrophysical and survey systematic uncertainties in modeling κ-PDF
- Appendices provide technical details related to masking effects on cosmic shear power spectrum and quantifying KS reconstruction impacts on moments/cumulants calculations

## Summary

Significant progress has been made in developing a theoretical framework for studying the statistics of cosmic large-scale structure, specifically focusing on weak-lensing one-point statistics in the mildly non-linear regime. This framework, known as the theory of large deviations (LDT), shows promise in modeling various aspects of the cosmic large-scale structure. The primary objective of a series of papers is to bridge the gap between theory and practical data analysis using LDT. In this first paper (Paper I) of the series, the authors demonstrate how to accurately model the Probability Distribution Function (PDF) of a reconstructed Kaiser-Squires convergence field under realistic conditions, such as those found in the third data release of the Dark Energy Survey (DES). They also address important factors like weak lensing systematics and higher-order lensing corrections due to intrinsic alignments, shear biases, photo-z errors, and baryonic feedback within their modeling approach. The upcoming work (Paper II) will focus on validating the robustness of their modeling through simulated likelihood analyses before applying it to actual observational data. The paper provides a comprehensive overview of the base model for true but observationally inaccessible convergence PDF from LDT, followed by detailing the Kaiser-Squires reconstruction procedure for κ field from a simulated full-sky shear field with a realistic mask. The modifications made to adapt the original LDT theoretical model to account for this reconstruction process are tested against N-body simulations. Additionally, strategies for incorporating higher-order lensing effects and addressing astrophysical and survey systematic uncertainties in modeling κ-PDF are presented. Finally, appendices delve into specific technical details related to masking effects on cosmic shear power spectrum and quantifying KS reconstruction impacts on moments/cumulants calculations. Overall, this work sets a solid foundation for further advancements in utilizing LDT for analyzing weak-lensing data in cosmological studies.