Quadratic estimators for CMB weak lensing - Antony Lewis.pdf (1.2 MB)
Quadratic estimators for CMB weak lensing
journal contribution
posted on 2023-06-10, 00:19 authored by Abhishek S Maniyar, Yacine Ali-Haïmoud, Julien Carron, Antony LewisAntony Lewis, Mathew S MadhavacherilIn recent years, weak lensing of the cosmic microwave background (CMB) has emerged as a powerful tool to probe fundamental physics, such as neutrino masses, primordial non-Gaussianity, dark energy, and modified gravity. The prime target of CMB lensing surveys is the lensing potential, which is reconstructed from the observed CMB temperature T and polarization E and B fields. Until very recently, this reconstruction has been performed with quadratic estimators (QEs), which, although known to be suboptimal for high-sensitivity experiments, are numerically efficient and useful to make forecasts and cross-check the results of more sophisticated likelihood-based methods. It is expected that ongoing and near-future CMB experiments, such as AdvACT, SPT-3G, and the Simons Observatory (SO), will also rely on QEs. In this work, we review different QEs and clarify and quantify their differences. In particular, we show that the Hu-Okamoto (HO02) estimator is not the absolute optimal lensing estimator that can be constructed out of quadratic combinations of T, E, and B fields. Instead, we derive the global-minimum-variance (GMV) lensing quadratic estimator. Although this estimator can be found elsewhere in the literature, it was erroneously described as equivalent to the HO02 estimator and has never been used in real data analyses. Here, we show explicitly that the HO02 estimator is suboptimal to the GMV estimator, with a reconstruction noise larger by up to ~9% for a SO-like experiment. We further show that the QE used in the Planck and recent SPT lensing analysis are suboptimal to both the HO02 and GMV estimator and would have a reconstruction noise up to ~11% larger than that of the GMV estimator for a SO-like experiment. In addition to clarifying differences between different QEs, this work should thus provide motivation to implement the GMV estimator in future lensing analyses relying on QEs.
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Publication status
- Published
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- Published version
Journal
Physical Review DISSN
2470-0010Publisher
American Physical SocietyExternal DOI
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8Volume
103Page range
1-13Article number
a083524Department affiliated with
- Physics and Astronomy Publications
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Peer reviewed?
- Yes
Legacy Posted Date
2021-07-12First Open Access (FOA) Date
2021-07-12First Compliant Deposit (FCD) Date
2021-07-09Usage metrics
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