Minimum variance estimation of galaxy power spectrum in redshift space
Abstract
We study an efficient way to enhance the measurability of the galaxy density and/or velocity power spectrum in redshift space. It is based on the angular decomposition with the tripolar spherical harmonic (TripoSH) basis and applicable even to galaxy distributions in wideangle galaxy surveys. While nontrivial multipolemode mixings are inevitable in the covariance of the Legendre decomposition coefficient commonly used in the smallangle power spectrum analysis, our analytical computation of the covariance of the TripoSH decomposition coefficient shows that such mixings are absent by virtue of high separability of the TripoSH basis, yielding the minimum variance. Via the simple signaltonoise ratio assessment, we confirm that the detectability improvement by the TripoSH decomposition approach becomes more significant at higher multipole modes, and the hexadecapole of the density power spectrum has two orders of magnitude improvement. The TripoSH decomposition approach is expected to be applied to not only currently available survey data but also forthcoming wideangle data, and to bring about something new or much more accurate cosmological information.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 November 2020
 DOI:
 10.1093/mnrasl/slaa132
 arXiv:
 arXiv:2005.03438
 Bibcode:
 2020MNRAS.498L..77S
 Keywords:

 methods: statistical;
 cosmology: observations;
 cosmology: theory;
 dark energy;
 dark matter;
 largescale structure of Universe;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 5 pages, 1 figure, 1 table