Effect of non-Gaussian lensing deflections on CMB lensing measurements

Abstract

We investigate the impact of non-Gaussian lensing deflections on measurements of the CMB lensing power spectrum. We find that the false assumption of their Gaussianity significantly biases these measurements in current and future experiments at the percent level. The bias is detected by comparing CMB lensing reconstructions from simulated CMB data lensed with Gaussian deflection fields to reconstructions from simulations lensed with fully non-Gaussian deflection fields. The non-Gaussian deflections are produced by ray-tracing through snapshots of an N-body simulation and capture both the non-Gaussianity induced by non-linear structure formation and by multiple correlated deflections. We find that the amplitude of the measured bias is in agreement with analytical predictions by . The bias is largest in temperature-based measurements and we do not find evidence for it in measurements from a combination of polarization fields (EB, EB). We argue that the non-Gaussian bias should be even more important for measurements of cross-correlations of CMB lensing with low-redshift tracers of large-scale structure.

A Measurement of the Cosmic Microwave Background Lensing Potential and Power Spectrum from 500 deg2 of SPTpol Temperature and Polarization Data

“…However, nonlinear structure growth and post-Born lensing would introduce non-Gaussianities to φ (Böhm et al 2016;Pratten & Lewis 2016). These non-Gaussianities produce the socalled N (3/2) L bias, as studied in Böhm et al (2016Böhm et al ( , 2018; Beck et al (2018). For the L range considered, the size of this bias is ∼0.5% for the temperature reconstruction and is negligible for the EB reconstruction for input CMB maps similar in noise levels and multipole range to those in this work (Böhm et al 2018;Beck et al 2018).…”

Baryonic effects on CMB lensing and neutrino mass constraints

“…To make good on this promise, however, upcoming lensing measurements will need to control for a plethora of systematics related to beam calibration [14], galactic and extragalactic foregrounds [15][16][17], and non-Gaussian clustering of the lenses [18,19]. In addition, we must have confidence in our modelling of the lensing signal itself.…”

Non-linear general relativistic effects in the observed redshift

“…While the procedure is similar to the linear one, a subtle difference exists: at the second order, the integration over the proper time λ can no longer be switched to an integration along the straight unperturbed geodesic, as the deviation from the straight path is also a linear order correction. These corrections are referred to as beyond the Born approximation or post-Born effects (see [37,38] for some studies about their impact on weak lensing galaxy surveys and [20][21][22][23][24][25][26] for their consequences on CMB spectra). Keeping this in mind, we have to express u µ in terms of second-order perturbations.…”

“…Moreover, the expression for the observed redshift is also directly applicable to the CMB on large scales. The possible impact of nonlinear corrections on the CMB spectra has been recently studied for the leading lensing terms from both the analytical [20][21][22][23][24][25][26] and numerical [27][28][29] point of view and discussed in the view of the next generation CMB experiments [30]. Non-linear calculations of the observed redshift along with others observables are important and have been already performed in literature by several collaborations.…”