CMB lensing
The integrated dark matter mass between the last-scattering surface (redshift 𝑧 ≃ 1100) and an observer at 𝑧 = 0 is responsible for the deflection of light in the primary CMB temperature anisotropies via the gravitational lensing effect. Lensing distorts the CMB 𝑇𝑇 power spectrum (temperature) and both distorts and mixes the 𝐸𝐸 and 𝐵𝐵 power spectra of the CMB polarization modes. This property can be exploited to reconstruct the gravitational lensing field using CMB quadratic estimators in 𝑇 (or 𝐸 and 𝐵). Much work has been devoted to developing optimal lensing quadratic estimators in harmonic space (e.g., Hu & Okamoto, ApJ 2002; Hirata & Seljak, PRD 2003). However, the kernel of the quadratic estimator in harmonic space is inherently non-local in real space, which implicitly requires a simultaneous analysis of the entire CMB sky, without any mask or missing data. In practice, though, CMB data are non-uniform over the sky: they contain non-uniform noise, as well as missing data in the Galactic plane, due to masking, which must be filled with fake CMB data ("inpainting") to allow full-sky analyses with standard quadratic estimators.
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CMB lensing reconstruction in real space
Bucher, Carvalho, Moodley, Remazeilles, PRD 85, 043016 (2012)
To ensure robust reconstruction of the lensing field from realistic CMB maps with missing data and non-uniform noise, it is necessary to construct estimator kernels that are localized in both harmonic and real (pixel) space. With this goal in mind, we explored the reconstruction of the lensing convergence and shear fields in real space by designing estimator kernels with limited support in real space, while retaining sufficient resolution in harmonic space to avoid losing statistical information relevant for the reconstruction of the lensing effect. Our analytical and numerical analyses showed that, for the Planck experiment, the support of our local estimator can be restricted to a disc of radius 1.5 degrees on the celestial sphere, without losing relevant information on the lensing effect compared to standard quadratic estimators. The local estimators developed in this work are particularly flexible and efficient for analyzing realistic CMB maps containing Galactic cuts and masked extragalactic point sources, as well as for ground-based CMB surveys with partial sky coverage.