Weak lensing power spectra for precision cosmology

Abstract

It is usually assumed that the ellipticity power spectrum measured in weak lensing observations can be expressed as an integral over the underlying matter power spectrum. This is true at order O(Φ 2 ) in the gravitational potential. We extend the standard calculation, constructing all corrections to order O(Φ 4 ). There are four types of corrections: corrections to the lensing shear due to multipledeflections; corrections due to the fact that shape distortions probe the reduced shear γ/(1 − κ) rather than the shear itself; corrections associated with the non-linear conversion of reduced shear to mean ellipticity; and corrections due to the fact that observational galaxy selection and shear measurement is based on galaxy brightnesses and sizes which have been (de)magnified by lensing. We show how the previously considered corrections to the shear power spectrum correspond to terms in our analysis, and highlight new terms that were not previously identified. All correction terms are given explicitly as integrals over the matter power spectrum, bispectrum, and trispectrum, and are numerically evaluated for the case of sources at z = 1. We find agreement with previous works for the O(Φ 3 ) terms. We find that for ambitious future surveys, the O(Φ 4 ) terms affect the power spectrum at the ∼1−5σ level; they will thus need to be accounted for, but are unlikely to represent a serious difficulty for weak lensing as a cosmological probe.

Estimating the weak-lensing rotation signal in radio cosmic shear surveys

“…This is the second order effect of the Born correction/lenslens coupling terms in the deflection angle (Krause & Hirata 2010). However, although this signal scales differently with l compared to the cosmic string signal considered here, it is below the level of this cosmic string signal on all scales and is unlikely to be detectable using currently planned radio surveys.…”

“…Furthermore, even on nonlinear scales in ΛCDM, the vector and tensor perturbations are negligible (Bruni et al 2014;Adamek et al 2014). At second order however, the scalar perturbations can generate rotation, through the term in the deflection angle that corresponds to the Born correction and lens-lens coupling (see Dodelson et al 2005;Krause & Hirata 2010;Thomas et al 2015). The size of this effect (and equivalently the size of the B-mode, see later) at second order in ΛCDM cosmologies has been examined in Krause & Hirata (2010) and Jain et al (2000) and found to be orders of magnitude smaller than the leading order signal.…”

“…The size of the second order effect in ΛCDM was calculated in Krause & Hirata (2010) and was found to be small. However, it is possible to generate the rotation mode to a greater magnitude in scenarios beyond ΛCDM.…”

Full-sky Gravitational Lensing Simulation for Large-area Galaxy Surveys and Cosmic Microwave Background Experiments

“…The solid red curve shows the theoretical prediction by CAMB, in which we employed the revised Halofit for the nonlinear matter power spectrum. The orange curve shows the leading correction to the Born approximation (the so-called "post-Born correction") predicted by the third-order perturbation of the gravitational potential (Krause & Hirata 2010). We also plot downward pointing cyan arrows to indicate typical angular resolutions of CMB experiments: ℓ ∼ 400 (θ ∼ 30 arcmin) for BI-CEP, Keck, and LiteBIRD; ℓ ∼ 2000 (θ ∼ 5 arcmin) for Planck; ℓ ∼ 4000 (θ ∼ 3 arcmin) for POLARBEAR and CMB-S4; ℓ ∼ 10 4 (θ ∼ 1 arcmin) for SPT and ACT.…”

A bias in cosmic shear from galaxy selection: results from ray-tracing simulations

“…Theoretical predictions for the shear correlation functions can be obtained from the matter power spectrum with relative ease (e.g. Bartelmann & Schneider 2001), but for the computation of the actually observable reduced shear correlation functions it is necessary to include higher-order corrections to the shear power spectrum (White 2005;Krause & Hirata 2010).…”