# Mapping dark matter on the celestial sphere with weak gravitational lensing

## TL;DR

This paper develops a method to recover convergence maps of dark matter directly on the celestial sphere using weak gravitational lensing, addressing limitations of planar approximations in large sky surveys.

## Contribution

It extends the Kaiser-Squires estimator to the spherical setting and demonstrates its effectiveness with simulations and real survey data.

## Key findings

- Projection effects can cause errors exceeding 50% in convergence maps.
- Stereographic projection best preserves local angles among planar methods.
- Direct spherical recovery avoids projection-induced errors entirely.

## Abstract

Convergence maps of the integrated matter distribution are a key science result from weak gravitational lensing surveys. To date, recovering convergence maps has been performed using a planar approximation of the celestial sphere. However, with the increasing area of sky covered by dark energy experiments, such as Euclid, the Large Synoptic Survey Telescope (LSST), and the Wide Field Infrared Survey Telescope (WFIRST), this assumption will no longer be valid. We recover convergence fields on the celestial sphere using an extension of the Kaiser-Squires estimator to the spherical setting. Through simulations we study the error introduced by planar approximations. Moreover, we examine how best to recover convergence maps in the planar setting, considering a variety of different projections and defining the local rotations that are required when projecting spin fields such as cosmic shear. For the sky coverages typical of future surveys, errors introduced by projection effects can be of order tens of percent, exceeding 50% in some cases. The stereographic projection, which is conformal and so preserves local angles, is the most effective planar projection. In any case, these errors can be avoided entirely by recovering convergence fields directly on the celestial sphere. We apply the spherical Kaiser-Squires mass-mapping method presented to the public Dark Energy Survey (DES) science verification data to recover convergence maps directly on the celestial sphere.