  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.

Cosmology and Nongalactic Astrophysics;Instrumentation and Methods for Astrophysics