The Angular Trispectra of CMB Temperature and Polarization

By T. Okamoto, Wayne Hu. 2002

148 citations recorded by the source corpus.

We develop the formalism necessary to study four-point functions of the cosmic microwave background (CMB) temperature and polarization elds. We determine the general form of CMB trispectra, with the constraints imposed by the assumption of statistical isotropy of the CMB elds, and derive expressions for their estimators, as well as their Gaussian noise properties. We apply these techniques to initial non-Gaussianity of a form motivated by in ationary models. Due to the large number of four-point con gurations, the sensitivity of the trispectra to initial non-Gaussianity approaches that of the temperature bispectrum at high multipole moment. These trispectra techniques will also be useful in the study of secondary anisotropies induced for example by the gravitational lensing of the CMB by the large scale structure of the universe.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/80f4d97f796122d9e64b46f2c495ce1d91848187

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Citations in the corpus

Delensing CMB polarization with external datasets (2010, background): “2 Temperature delensing Lens reconstruction estimators can also be used to estimate the lensing potential from CMB temperature measurements which extend to small angular scales [35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45].”
Measuring Primordial Non-Gaussianity in the Cosmic Microwave Background (2003, methodology): “The trispectrum can be as sensitive to fNL as the bispectrum (Okamoto & Hu 2002); however, we need more accurate predictions using the full radiation transfer function.”
3D weak lensing (2003, background): “The shear field, comprising γ1 and γ2, can be written as components of a tensor, and expanded in terms of tensor spherical harmonics, as in Taylor (2001), or spinspherical harmonics sY m ℓ as in Okamoto & Hu (2002).”
FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE OBSERVATIONS: COSMOLOGICAL INTERPRETATION (2008, unknown): “The analytical predictions for the Minkowski functionals (Hikage et al. 2006) and the angular trispectrum (the harmonic transform of the angular 4-point correlation function; Okamoto & Hu 2002; Kogo & Komatsu 2006) as a function of f localNL are available now.”
PRIMORDIAL NON-GAUSSIANITY, SCALE-DEPENDENT BIAS, AND THE BISPECTRUM OF GALAXIES (2009, background): “(15) The cubic-order term does not generate the bispectrum of CMB anisotropy or the matter density fluctuations at the leading order; however, it does generate the trispectrum, and the CMB trispectrum has been calculated by Okamoto & Hu (2002); Kogo & Komatsu (2006).”
Inflationary trispectrum from graviton exchange (2008, unknown): “The four-point correlation function is conventionally parametrized in terms of the trispectrum, written Tζ , and defined by [19, 20] 〈ζ(k1)ζ(k2)ζ(k3)ζ(k4)〉 = (2π)(3)δ( ∑”