Weak lensing of the CMB: A harmonic approach

By Wayne Hu. 2000

329 citations recorded by the source corpus.

Weak lensing of CMB anisotropies and polarization for the power spectra and higher order statistics can be handled directly in harmonic-space without recourse to real-space correlation functions. For the power spectra, this approach not only simplifies the calculations but is also readily generalized from the usual flat-sky approximation to the exact all-sky form by replacing Fourier harmonics with spherical harmonics. Counterintuitively, because of the nonlinear nature of the effect, errors in the flat-sky approximation do not improve on smaller scales. They remain at the 10% level through the acoustic regime and are sufficiently large to merit adoption of the all-sky formalism. For the bispectra, a cosmic variance limited detection of the correlation with secondary anisotropies has an order of magnitude greater signal-to-noise for combinations involving magnetic parity polarization than those involving the temperature alone. Detection of these bispectra will, however, be severely noise and foreground limited even with the Planck satellite, leaving room for improvement with higher sensitivity experiments. We also provide a general study of the correspondence between flat and all sky potentials, deflection angles, convergence and shear for the power spectra and bispectra.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/719d22197e4e4b7e92aed7dc8edb762a5a461fcb

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Citations in the corpus

Cosmology and Fundamental Physics with the Euclid Satellite (2012, background): “One can easily show that their angular power spectra satisfy the consistency relation, see [605]”
Planck 2018 results. IX. Constraints on primordial non-Gaussianity (2019, methodology): “The template of the lensing bispectrum7 is given by (Hu 2000; Lewis et al. 2011),”
The shear power spectrum from the COMBO-17 survey (2002, background): “In a spatially flat Universe, with comoving distancer we can relate the lensing potential and the gravitational potential by (e.g. Kaiser 1998; Hu 2000) φ(r) = 2 ∫ r 0 dr′ ( r − r′ rr′ ) Φ(r′).”
Sachs-Wolfe at second order: the CMB bispectrum on large angular scales (2009, background): “The derivation of these expressions can be found in [32].”
The impact of non‐Gaussian errors on weak lensing surveys (2008, methodology): “Therefore non-Gaussian errors can be significant in weak lensing measurements as indicated by a few previous studies based on ray tracing simulations (White & Hu 2000; Semboloniet al. 2007) and the halo model approach (Cooray & Hu 2001; Pielorz 2008).”
Shadow cast and deflection angle of Kerr-Newman-Kasuya spacetime (2018, background): “Moreover, in “weak lensing” the effect is much weaker but can still be detected statistically [72].”
Detection of Non-Gaussianity in the Wilkinson Microwave Anisotropy Probe First-Year Data Using Spherical Wavelets (2003, background): “…of the universe (Ostriker & Vishniac 1986; Aghanim et al. 1996), the Rees-Sciama effect due to the nonlinear evolution of the large-scale structure (Rees & Sciama 1968; Martı́nez-González & Sanz 1990), gravitational lensing (Martı́nez-González et al. 1997; Hu 2000; Goldberg & Spergel 1999), etc.”
Gravitational lensing (2010, background): “It was pointed out that lensing of the CMB must be treated in spherical geometry on the full sky [74, 75, 211, 373] if per centlevel accuracy is to be achieved.”
Cosmological parameters from lensing power spectrum and bispectrum tomography (2003, background): “The expression for the bispectrum of the convergence field involves the Wigner-3j symbol, which has a closed algebraic form (e.g., Hu 2000): c© 0000 RAS, MNRAS000, 1–19 ( l1 l2 l3 0 0 0 ) = (−1)L/2 (L 2 )!”
Planck 2015 results. XVII. Constraints on primordial non-Gaussianity (2015, unknown): “The template is given by (Hu 2000; Lewis et al. 2011) bX1X2X3,LISW `1`2`3 = CX2φ `2 C̃X1X3 `3 f X1 `1`2`3 + CX3φ `3 C̃X1X2 `2 f X1 `1`3`2 + CX1φ `1 C̃X2X3 `3 f X2 `2`1`3 + CX3φ `3 C̃X1X2 `1 f X2 `2`3`1 + CX1φ `1 C̃X2X3 `2 f X3 `3`1`2 + CX2φ `2 C̃X1X3 `1 f X3 `3`2`1 .”
Delensing CMB polarization with external datasets (2010, background): “In the limit of small instrumental noise, the largest “guaranteed” source of B-mode power on large angular scales is gravitational lensing by large-scale structure, which converts the E-modes generated during recombination to a mixture of E and B [12, 13].”
Algorithms for bispectra: Forecasting, optimal analysis, and simulation (2006, methodology): “…theoretically motivated bispectra from secondary anisotropies (Goldberg & Spergel 1999; Seljak & Zaldarriaga 1999; Spergel & Goldberg 1999; Cooray & Hu 2000; Hu 2000b; Verde & Spergel 2002) and early universe physics (Alishahiha et al. 2004; Rigopoulos et al. 2006, 2007; Chen et al. 2007a,b),…”
DeepCMB: Lensing Reconstruction of the Cosmic Microwave Background with Deep Neural Networks (2018, background): “…scattering surface to us, their paths are deflected by the gradient of the gravitational potential φ, an effect called gravitational lensing: X̃±(n̂) = X±(n̂+∇φ(n̂)), (1) where X is the unlensed field and X̃ denotes the lensed field (e.g., Hu, 2000) and X± = Q ± iU . for the polarization fields.”