The Limits of Cosmic Shear

TL;DR

This paper examines the common approximations used in cosmic shear analysis, revealing that they can cause significant power suppression and advocating for more accurate, non-approximated methods to improve future cosmological measurements.

Contribution

It identifies the limitations of standard approximations in cosmic shear studies and proposes a fully non-approximated analysis approach for more accurate results.

Findings

Approximations can suppress power by over 1% on large scales.

Unaccounted effects could contribute at least 11% to systematic errors in Euclid-like surveys.

Using full spherical-sky and non-Limber methods improves accuracy.

Abstract

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% 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% of the total budget for systematic effects for a power spectrum analysis of a Euclid-like experiment; but they are unnecessary.