All-Sky Analysis of the General Relativistic Galaxy Power Spectrum
  We perform an all-sky analysis of the general relativistic galaxy power
spectrum using the well-developed spherical Fourier decomposition. Spherical
Fourier analysis expresses the observed galaxy fluctuation in terms of the
spherical harmonics and spherical Bessel functions that are angular and radial
eigenfunctions of the Helmholtz equation, providing a natural orthogonal basis
for all-sky analysis of the large-scale mode measurements. Accounting for all
the relativistic effects in galaxy clustering, we compute the spherical power
spectrum and its covariance matrix and compare it to the standard
three-dimensional power spectrum to establish a connection. The spherical power
spectrum recovers the three-dimensional power spectrum at each wavenumber k
with its angular dependence mu_k encoded in angular multipole l, and the
contributions of the line-of-sight projection to galaxy clustering such as the
gravitational lensing effect can be readily accommodated in the spherical
Fourier analysis. A complete list of formulas for computing the relativistic
spherical galaxy power spectrum is also presented.
