Minimum variance estimation of galaxy power spectrum in redshift space
  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 wide-angle galaxy surveys. While
nontrivial multipole-mode mixings are inevitable in the covariance of the
Legendre decomposition coefficient commonly used in the small-angle power
spectrum analysis, our analytic 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 signal-to-noise ratio assessment, we confirm that the detectability
improvement by the TripoSH decomposition approach becomes more significant at
higher multipole modes, and, e.g., 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 wide-angle one, and to bring about something new or much
more accurate cosmological information.
