Full-Sky Lensing Reconstruction of 21 cm Intensity Maps
  Weak gravitational lensing of the 21 cm radiation is expected to be an
important cosmological probe for post-reionization physics. We investigate the
reconstruction of the matter density perturbations using a quadratic minimum
variance estimator. The next generation of line intensity mapping (LIM) surveys
such as HIRAX and CHIME will cover a larger sky fraction, which requires one to
account for the curvature in the sky. Thus, we extend the plane-parallel
flat-sky formalism for lensing reconstruction to account for a full-sky survey
using the Spherical Fourier-Bessel (SFB) expansion. Using the HIRAX 21 cm
survey as a basis, we make predictions for lensing-reconstruction noise in our
formalism and compare our results with the predictions from the plane-parallel
formalism. We find agreement with the plane-parallel noise power spectrum at
small scales and a significant deviation at scales $L\lesssim \ell_{\rm
res}-k_{\rm eq}R$ where $R$ is the radius of the shell volume, $k_{\rm eq}$ is
the wavenumber for matter-radiation equality, and $\ell_{\rm res}$ is the
angular resolution scale. Furthermore, we derive the SFB flat-sky
reconstruction noise and compare it with the full-sky SFB case as well as the
plane-parallel case, finding minor deviations from the full-sky noise due to
sphericity. We also determine that, in the absence of non-Gaussian statistics
of the intensity field but accounting for foregrounds, the signal-to-noise
ratio (SNR) for $C_\ell^{\phi\phi}$ using our SFB estimator increases by 107%.
This shows that accounting for the curved sky in LIM weak lensing will be
crucial for large-scale cosmology.
