2001/05/31 by Wayne Hu · 4 citations
Mathematics · Physics and Astronomy · #Anisotropy #Astrophysics #Cosmic microwave background #Cosmic variance #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Galaxy #Mathematics #Non-Gaussianity #Physics #Planck #Quantum mechanics #Redshift #Scientific Research and Discoveries #Spectral density #Statistics #Strong gravitational lensing #Trispectrum #Weak gravitational lensing #astro-ph
paper · pdf · doi:10.1103/physrevd.64.083005
published as Phys.Rev. D64 (2001) 083005 · 21 pages, 5 figures, errata typos in Eqn 35, 41, 70, A10 corrected. no conclusions changed
openalex publication_date 2001/09/11 · arxiv created 2004/02/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the general properties of the cosmic microwave background temperature four-point function, specifically its harmonic analogue, the angular trispectrum, and illustrate its utility in finding optimal quadratic statistics through the weak gravitational lensing effect. We determine the general form of the trispectrum, under the assumptions of rotational, permutation, and parity invariance, its estimators on the sky, and their Gaussian noise properties. The signal-to-noise in the trispectrum can be highly configuration dependent and any quadratic statistic used to compress the information to a manageable two-point level must be carefully chosen. Through a systematic study, we determine that for the case of lensing a specific statistic, the divergence of a filtered temperature-weighted temperature-gradient map contains the maximal signal-to-noise and reduces the variance of estimates of the large-scale convergence power spectrum by over an order of magnitude over previous gradient-gradient techniques. The total signal-to-noise for lensing with the Planck satellite is of order 60 for a fiducial cold dark matter model with a cosmological constant (\ensuremathΛCDM).