Statistics of cosmic microwave background polarization

1996/11/15 by Marc Kamionkowski, Arthur Kosowsky, Albert Stebbins · 1,021 citations
Chemistry · Mathematics · Physics and Astronomy · #Anisotropy #Astrophysics and Cosmic Phenomena #Chemistry #Computational physics #Cosmic microwave background #Cosmology and Gravitation Theories #Fast multipole method #Mathematical analysis #Mathematics #Multipole expansion #Physics #Planck #Polarization (electrochemistry) #Quantum mechanics #Radio Astronomy Observations and Technology #Spherical harmonics #Spherical multipole moments #astro-ph #hep-ph

paper · pdf · doi:10.1103/physrevd.55.7368

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 55(12), 7368-7388 (American Physical Society) · 28 pages, RevTeX

arxiv created 1996/11/15 · openalex publication_date 1997/06/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present a formalism for analyzing a full-sky temperature and polarization map of the cosmic microwave background. Temperature maps are analyzed by expanding over the set of spherical harmonics to give multipole moments of the two-point correlation function. Polarization, which is described by a second-rank tensor, can be treated analogously by expanding in the appropriate tensor spherical harmonics. We provide expressions for the complete set of temperature and polarization multipole moments for scalar and tensor metric perturbations. Four sets of multipole moments completely describe isotropic temperature and polarization correlations; for scalar metric perturbations one set is identically zero, giving the possibility of a clean determination of the vector and tensor contributions. The variance with which the multipole moments can be measured in idealized experiments is evaluated, including the effects of detector noise, sky coverage, and beam width. Finally, we construct coordinate-independent polarization two-point correlation functions, express them in terms of the multipole moments, and derive small-angle limits.

Citations

• Signature of Gravity Waves in the Polarization of the Microwave Background
• Small-scale cosmic microwave background anisotropies as probe of the geometry of the universe
• Multipole expansions of gravitational radiation
• Gravitational waves and the polarization of the cosmic microwave background
• Note on the Bondi-Metzner-Sachs Group
• Polarization of the microwave background in reionized models

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