3D Photometric Cosmic Shear

TL;DR

This paper improves 3D cosmic shear analysis by incorporating photometric redshift distributions directly, simplifying calculations with the Limber approximation, and clarifying the connection between tomography and 3D shear for better cosmological constraints.

Contribution

It introduces methods to include individual galaxy redshift probabilities directly and explores the use of the Limber approximation in 3D cosmic shear analysis.

Findings

Photometric redshift distributions can be directly integrated into 3D shear analysis.

The Limber approximation simplifies 3D cosmic shear calculations and has a specific range of applicability.

Different advantages of 3D cosmic shear and tomography are clarified, with suggestions for combining their strengths.

Abstract

Here we present a number of improvements to weak lensing 3D power spectrum analysis, 3D cosmic shear, that uses the shape and redshift information of every galaxy to constrain cosmological parameters. We show how photometric redshift probability distributions for individual galaxies can be directly included in this statistic with no averaging. We also include the Limber approximation, considerably simplifying full 3D cosmic shear analysis, and we investigate its range of applicability. Finally we show the relationship between weak lensing tomography and the 3D cosmic shear field itself; the steps connecting them being the Limber approximation, a harmonic-space transform and a discretisation in wavenumber. Each method has its advantages: 3D cosmic shear analysis allows straightforward inclusion of all relevant modes, thus ensuring minimum error bars, and direct control of the range of physical wavenumbers probed, to avoid the uncertain highly nonlinear regime. On the other hand, tomography is more convenient for checking systematics through direct investigation of the redshift dependence of the signal. Finally, for tomography, we suggest that the angular modes probed should be redshift-dependent, to recover some of the 3D advantages.