The Limits of Cosmic Shear

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.

15 pages, accepted to MNRAS

References in corpus (12)

• Wide-Field InfrarRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA 2015 Report
• KiDS-450: Cosmological parameter constraints from tomographic weak gravitational lensing
• Dark energy constraints from cosmic shear power spectra: impact of intrinsic alignments on photometric redshift requirements
• Extended Limber Approximation
• Systematic Bias in Cosmic Shear: Beyond the Fisher Matrix
• How accurate is Limber's equation?
• Measuring dark energy properties with 3D cosmic shear
• Cosmological constraints from COMBO-17 using 3D weak lensing
• Shear Power Spectrum Reconstruction using Pseudo-Spectrum Method
• Cosmological parameters, shear maps and power spectra from CFHTLenS using Bayesian hierarchical inference
• Cross-correlation of weak lensing and gamma rays: implications for the nature of dark matter
• Cosmic Shear as a Probe of Galaxy Formation Physics

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