Fast spin ±2 spherical harmonics transforms and application in cosmology
Abstract
A fast and exact algorithm is developed for the spin ±2 spherical harmonics transforms on equiangular pixelizations on the sphere. It is based on the Driscoll and Healy fast scalar spherical harmonics transform. The theoretical exactness of the transform relies on a sampling theorem. The associated asymptotic complexity is of order O (L^{2} log_{2}^{2} L) , where 2L stands for the squareroot of the number of sampling points on the sphere, also setting a band limit L for the spin ±2 functions considered. The algorithm is presented as an alternative to existing fast algorithms with an asymptotic complexity of order O (L^{3}) on other pixelizations. We also illustrate these generic developments through their application in cosmology, for the analysis of the cosmic microwave background (CMB) polarization data.
 Publication:

Journal of Computational Physics
 Pub Date:
 October 2007
 DOI:
 10.1016/j.jcp.2007.07.005
 arXiv:
 arXiv:astroph/0508514
 Bibcode:
 2007JCoPh.226.2359W
 Keywords:

 Astrophysics;
 General Relativity and Quantum Cosmology;
 Mathematical Physics
 EPrint:
 20 pages, 2 figures. Version accepted for publication in J. Comput. Phys.