Spherical Harmonic Analyses of Intensity Mapping Power Spectra
  Intensity mapping is a promising technique for surveying the large scale
structure of our Universe from $z=0$ to $z \sim 150$, using the brightness
temperature field of spectral lines to directly observe previously unexplored
portions of out cosmic timeline. Examples of targeted lines include the
$21\,\textrm{cm}$ hyperfine transition of neutral hydrogen, rotational lines of
carbon monoxide, and fine structure lines of singly ionized carbon. Recent
efforts have focused on detections of the power spectrum of spatial
fluctuations, but have been hindered by systematics such as foreground
contamination. This has motivated the decomposition of data into Fourier modes
perpendicular and parallel to the line-of-sight, which has been shown to be a
particularly powerful way to diagnose systematics. However, such a method is
well-defined only in the limit of a narrow-field, flat-sky approximation. This
limits the sensitivity of intensity mapping experiments, as it means that wide
surveys must be separately analyzed as a patchwork of smaller fields. In this
paper, we develop a framework for analyzing intensity mapping data in a
spherical Fourier-Bessel basis, which incorporates curved sky effects without
difficulty. We use our framework to generalize a number of techniques in
intensity mapping data analysis from the flat sky to the curved sky. These
include visibility-based estimators for the power spectrum, treatments of
interloper lines, and the "foreground wedge" signature of spectrally smooth
foregrounds.
