The shape of the CMB lensing bispectrum

By A. Lewis, A. Challinor, D. Hanson. 2011

150 citations recorded by the source corpus.

Lensing of the CMB generates a significant bispectrum, which should be detected by the Planck satellite at the 5-sigma level and is potentially a non-negligible source of bias for fNL estimators of local non-Gaussianity. We extend current understanding of the lensing bispectrum in several directions: (1) we perform a non-perturbative calculation of the lensing bispectrum which is ~ 10% more accurate than previous, first-order calculations; (2) we demonstrate how to incorporate the signal variance of the lensing bispectrum into estimates of its amplitude, providing a good analytical explanation for previous Monte-Carlo results; and (3) we discover the existence of a significant lensing bispectrum in polarization, due to a previously-unnoticed correlation between the lensing potential and E-polarization as large as 30% at low multipoles. We use this improved understanding of the lensing bispectra to re-evaluate Fisher-matrix predictions, both for Planck and cosmic variance limited data. We confirm that the non-negligible lensing-induced bias for estimation of local non-Gaussianity should be robustly treatable, and will only inflate fNL error bars by a few percent over predictions where lensing effects are completely ignored (but note that lensing must still be accounted for to obtain unbiased constraints). We also show that the detection significance for the lensing bispectrum itself is ultimately limited to 9 sigma by cosmic variance. The tools that we develop for non-perturbative calculation of the lensing bispectrum are directly relevant to other calculations, and we give an explicit construction of a simple non-perturbative quadratic estimator for the lensing potential and relate its cross-correlation power spectrum to the bispectrum. Our numerical codes are publicly available as part of CAMB and LensPix.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/24f6f2094ac8664cd3aac6f07173b4c3d48f758d

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Citations in the corpus

COrE (Cosmic Origins Explorer) A White Paper (2011, methodology): “Beyond searches for primordial NG, COrE will also see NG imprinted on the CMB maps by the lensing/ISW correlation [70, 71, 72].”
The Atacama Cosmology Telescope: A Measurement of the DR6 CMB Lensing Power Spectrum and Its Implications for Structure Growth (2023, methodology): “…to the SQE estimator from Maniyar et al. (2021), which is slightly sub-optimal compared to Okamoto & Hu (2003). sub-percent levels; however, for the TT estimator, we use the lensed temperature-gradient power spectrum CT∇T` to further improve the fidelity of the reconstruction (Lewis et al. 2011).”
Planck 2018 results. IX. Constraints on primordial non-Gaussianity (2019, methodology): “CMB lensing generates a significant CMB bispectrum (Hanson & Lewis 2009; Mangilli & Verde 2009; Lewis et al. 2011; Mangilli et al. 2013).”
Primordial Non-Gaussianity (2019, background): “[137] Antony Lewis, Anthony Challinor, and Duncan Hanson.”
Planck2018 results (2018, background): “(2) to make the estimator nearly unbiased to non-perturbative order (Hanson et al. 2011; Lewis et al. 2011).”
Planck 2015 results. XVII. Constraints on primordial non-Gaussianity (2015, unknown): “However, as explained in Lewis et al. (2011), there is an important correlation between the lensing potential and the large-scale E-polarization generated by scattering at reionization.”
CMB-S4 Science Case, Reference Design, and Project Plan (2019, unknown): “[128]); some secondaries are expected (see Ref.”
NINE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: FINAL MAPS AND RESULTS (2012, methodology): “The ISWlensing bias was computed using the Fisher matrix approximation, but this has been shown to be an excellent approximation to the exact result (Hanson et al. 2009; Lewis et al. 2011).”