2007/03/31 by Raphael Flauger, Steven Weinberg · 1 citation
Mathematics · Physics and Astronomy · #Anisotropy #Astrophysics and Cosmic Phenomena #Cosmic microwave background #Cosmology and Gravitation Theories #Fast multipole method #Geometry #Mathematical physics #Mathematics #Multipole expansion #Order (exchange) #Physics #Quantum mechanics #Radio Astronomy Observations and Technology #Spherical multipole moments #Tensor (intrinsic definition) #astro-ph
paper · pdf · doi:10.1103/physrevd.75.123505
published as Phys.Rev.D75:123505,2007 · 19 pages, 9 figures, accepted for publication in Phys. Rev. D, references and comments on earlier work on the subject added, cosmetic modification of figures
arxiv created 2007/05/11 · openalex publication_date 2007/06/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present approximate formulas for the tensor BB, EE, TT, and TE multipole coefficients for large multipole order \ensuremathℓ. The error in using the approximate formula for the BB multipole coefficients is less than cosmic variance for \ensuremathℓ>10. These approximate formulas make various qualitative properties of the calculated multipole coefficients transparent: specifically, they show that, whatever values are chosen for cosmological parameters, the tensor EE multipole coefficients will always be larger than the BB coefficients for all \ensuremathℓ>15, and that these coefficients will approach each other for \ensuremathℓ\ensuremath≪100. These approximations also make clear how these multipole coefficients depend on cosmological parameters.