Angular trispectrum of the cosmic microwave background
Abstract
We study the general properties of the cosmic microwave background temperature fourpoint 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 signaltonoise in the trispectrum can be highly configuration dependent and any quadratic statistic used to compress the information to a manageable twopoint 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 temperatureweighted temperaturegradient map contains the maximal signaltonoise and reduces the variance of estimates of the largescale convergence power spectrum by over an order of magnitude over previous gradientgradient techniques. The total signaltonoise for lensing with the Planck satellite is of order 60 for a fiducial cold dark matter model with a cosmological constant (ΛCDM).
 Publication:

Physical Review D
 Pub Date:
 October 2001
 DOI:
 10.1103/PhysRevD.64.083005
 arXiv:
 arXiv:astroph/0105117
 Bibcode:
 2001PhRvD..64h3005H
 Keywords:

 98.70.Vc;
 Background radiations;
 Astrophysics
 EPrint:
 21 pages, 5 figures, errata typos in Eqn 35, 41, 70, A10 corrected. no conclusions changed