Angular Spectra for non-Gaussian Isotropic Fields
Gyorgy Terdik
TL;DR
This paper develops a theoretical framework for analyzing the isotropy of non-Gaussian cosmic microwave background fields using spectra, providing formulas for higher-order spectra and covariances.
Contribution
It introduces necessary and sufficient conditions for isotropy in non-Gaussian fields and derives explicit formulas for higher-order spectra and covariances.
Findings
Necessary and sufficient condition for isotropy in non-Gaussian fields
Explicit formulas for bispectrum, trispectrum, and higher-order spectra
Framework applicable to CMB anisotropy analysis
Abstract
Cosmic Microwave Background (CMB) Anisotropies is a subject of intensive research in several fields of sciences. In this paper we start a systematic development of basic notions and theory in statistics according to the application for CMB. The main result of this paper is the necessary and sufficient condition for isotropy of a non-Gaussian field in terms of spectra. Clear formulae for bi-, tri- and polyspectra and bi-, tri-, and higher order covariances are also given. Keywords: Bispectrum, Trispectrum, Angular poly-Spectra, Cosmic microwave background radiation; Gaussianity; spherical random fields
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