CMB lensing and primordial non-Gaussianity

TL;DR

This study assesses how gravitational lensing affects the estimation of primordial non-Gaussianity from the CMB bispectrum, focusing on ISW-lensing bias and lensing-induced shape changes. Using analytic low-order results and extensive non-Gaussian simulations with Planck-like $\ell_{max}$, the authors show that the ISW-lensing bias is a significant contaminant for the local shape but is manageable with subtraction, while lensing-induced modifications to the bispectrum shape have only small impact on $f_{NL}$ normalization. They demonstrate that the lensed bispectrum smears acoustic features by about 10% and that the resulting increase in estimator variance is negligible for Planck, implying robust constraints on $f_{NL}^{\rm loc}$ and $f_{NL}^{\rm eq}$ in this regime. Overall, lensing does not substantially degrade Planck-like measurements of primordial non-Gaussianity when biases are properly accounted, and the results support continued use of standard Fisher-forecast techniques with lensed simulations for future analyses.

Abstract

We study the effects of gravitational lensing on the estimation of non-Gaussianity from the bispectrum of the cosmic microwave background (CMB) temperature anisotropies. We find that the effect of lensing on the bispectrum may qualitatively be described as a smoothing of the acoustic features analogous to the temperature power spectrum. In contrast to previous results, for a Planck-like experiment which is cosmic-variance limited to L=2000, we find that lensing causes no significant degradation of our ability to constrain the non-Gaussianity amplitude fNL for both local and equilateral configurations, provided that the biases due to the cross correlation between the lensing potential and the integrated-Sachs-Wolfe (ISW) contribution to the CMB temperature are adequately understood. With numerical simulations, we also verify that low-order Taylor approximations to the lensed bispectrum and ISW-lensing biases are accurate.

Figures (3)

• Figure 1: Biases in $f_{NL}^X$ for the local (top) and equilateral (bottom) shapes if the ISW-lensing cross correlation were to be ignored. The analysis is assumed cosmic-variance limited up to a maximum multipole $\ell_{\rm max}$. The solid/dotted lines are calculated from Eq. (\ref{['eq:isw_lensing_lowest_order']}) and are shown dotted where the bias is negative. Long-dashed lines are the expected Gaussian errors on $f_{NL}^X$ computed from the Fisher matrix.
• Figure 2: A "slice" $B_{\ell,\ell+10,10}$ through the local bispectrum for $f_{NL}=1$. The simulations are unlensed (magenta line) and lensed (cyan line) with $C_{\ell}^{T\phi} = 0$, while the first-order analytical predictions are solid black (unlensed) and dashed black (lensed) lines. The Monte-Carlo results use 1000 simulations. The fractional effect due to lensing is shown in the bottom panel for the simulations (red line) and the first-order analytic result (black line).
• Figure 3: Power spectrum of the non-Gaussian component $a_{\ell m}^{NG,\text{loc}}$ in the local model from three different simulation techniques: (1) uses the "exact" simulation algorithm of Liguori:2003mb; (2) uses the general algorithm of Eq. (\ref{['eq:alm_sim_local']}); and (3) uses the modified algorithm of Eq. (\ref{['eq:sim_local']}).