Precision calculations of the cosmic shear power spectrum projection

Martin Kilbinger, Catherine Heymans, Marika Asgari, Shahab Joudaki, Peter Schneider, Patrick Simon, Ludovic Van Waerbeke, Joachim Harnois-Déraps, Hendrik Hildebrandt, Fabian Köhlinger, Konrad Kuijken, Massimo Viola

Research output: Contribution to journalArticlepeer-review

Abstract

We compute the spherical-sky weak-lensing power spectrum of the shear and convergence. We discuss various approximations, such as flat-sky, and first- and second- order Limber equations for the projection. We find that the impact of adopting these approximations are negligible when constraining cosmological parameters from current weak lensing surveys. This is demonstrated using data from the Canada-France-Hawaii Lensing Survey (CFHTLenS). We find that the reported tension with Planck Cosmic Microwave Background (CMB) temperature anisotropy results cannot be alleviated, in contrast to the recent claim made by Kitching et al. (2016, version 1). For future large-scale surveys with unprecedented precision, we show that the spherical second-order Limber approximation will provide sufficient accuracy. In this case, the cosmic-shear power spectrum is shown to be in agreement with the full projection at the sub-percent level for l > 3, with the corresponding errors an order of magnitude below cosmic variance for all l. When computing the two-point shear correlation function, we show that the flat-sky fast Hankel transformation results in errors below two percent compared to the full spherical transformation. In the spirit of reproducible research, our numerical implementation of all approximations and the full projection are publicly available within the package nicaea at http://www.cosmostat.org/software/nicaea.
Original languageEnglish
Pages (from-to)2126-2141
JournalMonthly Notices of the Royal Astronomical Society
Volume472
Issue number2
DOIs
Publication statusPublished - 23 Aug 2017

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