The limits of cosmic shear

In this paper, we discuss the commonly used limiting cases, or approximations, for two-point cosmic-shear statistics. We discuss the most prominent assumptions in this statistic: the flat-sky (small angle limit), the Limber (Bessel-to-delta function limit) and the Hankel transform (large ℓ-mode limit) approximations; that the vast majority of cosmic-shear results to date have used simultaneously. We find that the combined effect of these approximations can suppress power by ≳ 1 per cent on scales of ℓ ≲ 40. A fully non-approximated cosmic-shear study should use a spherical-sky, non-Limber-approximated power spectrum analysis and a transform involving Wigner small-d matrices in place of the Hankel transform. These effects, unaccounted for, would constitute at least 11 per cent of the total budget for systematic effects for a power spectrum analysis of a Euclid-like experiment; but they are unnecessary.