Game of cones: A nulling strategy for modelling lensing convergence in cones with large deviation theory

TL;DR

This paper introduces a large-deviation theory-based nulling strategy for modeling lensing convergence in cones, accurately capturing non-Gaussian features and improving analysis of weak-lensing data for cosmological surveys.

Contribution

It develops a first-principles large-deviation model for lensing convergence that accounts for cone geometry and introduces a nulling procedure to enhance validity in tomographic analyses.

Findings

Model matches numerical simulations within 5% in tails at redshift 1

Analytical approximation enables practical implementation

Nulling procedure improves accuracy for tomographic weak-lensing analysis

Abstract

The distribution of the cosmic convergence field is modeled using a large-deviation principle where all non-Gaussian contributions are computed from first principles. The geometry of the past light cone is accounted for by constructing the total weak-lensing signal from contributions of the matter density in thin disk slices. The prediction of this model is successfully tested against numerical simulation with ray tracing, and found to be accurate within at least 5 per cent in the tails at redshift 1 and opening angle of 10 arcmin and even more so with increasing source redshift and opening angle. An accurate analytical approximation to the theory is also provided for practical implementation. The lensing kernel that mixes physical scales along the line-of-sight tends to reduce the domain of validity of this theoretical approach compared to the three dimensional case of cosmic densities in spherical cells. This effect is shown to be avoidable if a nulling procedure is implemented in order to localise the lensing line-of-sight integrations in a tomographic analysis. Accuracy in the tails is thus achieved within a percent for source redshifts between 0.5 and 1.5 and an opening angle of 10 arcmin. Applications to future weak-lensing surveys like Euclid and the specific issue of shape noise are discussed.