The Angular Trispectrum of the CMB

By Wayne Hu. 2001

145 citations recorded by the source corpus.

We study the general properties of the CMB 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 LCDM cosmology.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9704b62468b96c523f2a8519085cc58a20acd7b9

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In Astronomy and Astrophysics

In Statistical and Nonlinear Physics

Citations in the corpus

Planck 2013 results. XVI. Cosmological parameters (2013, background): “In the context of lensing reconstruction, the CMB trispectrum due to lensing takes the form T`1`2 `3`4 (L) ≈ CφφL C TT `2 CTT`4 F`1L`2 F`3L`4 , (39) where CTT` is the lensed temperature power spectrum and F`1L`2 is a geometric mode-coupling function (Hu 2001; Hanson et al. 2011).”
The Sunyaev-Zel'dovich angular power spectrum as a probe of cosmological parameters (2002, background): “A angular-trispectrum configuration is represented by a quadrilateral, and is characterized by four sides and one diagonal (Hu 2001).”
Observational probes of cosmic acceleration (2012, methodology): “These products of temperature modes can be used as estimators of the lensing potential (Hu, 2001).”
Inflationary trispectrum from graviton exchange (2008, background): “It is possible that interesting information might be encoded in the higher-order npoint functions, such as the connected part of the four-point function [14].”