On Weak Lensing Response Functions

TL;DR

This paper develops a response function approach within the separate universe formalism to model weak lensing statistics, extending previous work to arbitrary order and incorporating line-of-sight effects, with applications to 3D and tomographic analyses.

Contribution

It introduces a novel RFs framework for weak lensing, including high-order spectra and real-space counterparts, enhancing modeling capabilities for survey data.

Findings

RFs extend to arbitrary order, including bispectrum and trispectrum.

Line-of-sight effects cause RFs to differ from squeezed correlation functions.

The spherical Fourier-Bessel formalism enables 3D and tomographic applications.

Abstract

We introduce the response function (RFs) approach to model the weak lensing statistics in the context of separate universe formalism. Numerical results for the RFs are presented for various semi-analytical models that include perturbative modelling and variants of halo models. These results extend the recent studies of the Integrated Bispectrum (IB) and Trispectrum to arbitrary order. We find that due to the line-of-sight (los) projection effects, the expressions for RFs are not identical to the squeezed correlation functions of the same order. We compute the RFs in three-dimensions (3D) using the spherical Fourier-Bessel (sFB) formalism which provides a natural framework for incorporating photometric redshifts, and relate these expressions to tomographic and projected statistics. We generalise the concept of $k$-cut power spectrum to $k$-cut response functions. In addition to the response function for high-order spectra, we also define their counterparts in real space, since they are easier to estimate from surveys with low sky-coverage and non-trivial survey boundaries.