Post-Limber Weak Lensing Bispectrum, Reduced Shear Correction, and Magnification Bias Correction

Abstract

The significant increase in precision that will be achieved by Stage IV cosmic shear surveys means that several currently used theoretical approximations may cease to be valid. An additional layer of complexity arises from the fact that many of these approximations are interdependent; the procedure to correct for one involves making another. Two such approximations that must be relaxed for upcoming experiments are the reduced shear approximation and the effect of neglecting magnification bias. Accomplishing this involves the calculation of the convergence bispectrum; typically subject to the Limber approximation. In this work, we compute the post-Limber convergence bispectrum, and the post-Limber reduced shear and magnification bias corrections to the angular power spectrum for a Euclid-like survey. We find that the Limber approximation significantly overestimates the bispectrum when any side of the bispectrum triangle, ${\ell }_i<60$. However, the resulting changes in the reduced shear and magnification bias corrections are well below the sample variance for $\ell \le 5000$. We also compute a worst-case scenario for the additional biases on $w_0{w}_a$CDM cosmological parameters that result from the difference between the post-Limber and Limber approximated forms of the corrections. These further demonstrate that the reduced shear and magnification bias corrections can safely be treated under the Limber approximation for upcoming surveys.

12 pages, 4 figures. Accepted by Phys. Rev. D. Matches published version

References in corpus (6)

• Dark energy constraints from cosmic shear power spectra: impact of intrinsic alignments on photometric redshift requirements
• Cosmology with Weak Lensing Surveys
• The Wide Field Infrared Survey Telescope: 100 Hubbles for the 2020s
• Probing dark energy with the shear-ratio geometric test
• Anisotropic Magnification Distortion of the 3D Galaxy Correlation: I. Real Space
• Lensing Bias in Cosmic Shear

Cited by in corpus (1)

• Parameter Inference for Weak Lensing using Gaussian Processes and MOPED