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Weak gravitational lensing of the 21 cm radiation is expected to be animportant cosmological probe for post-reionization physics. We investigate thereconstruction of the matter density perturbations using a quadratic minimumvariance estimator. The next generation of line intensity mapping (LIM) surveyssuch as HIRAX and CHIME will cover a larger sky fraction, which requires one toaccount for the curvature in the sky. Thus, we extend the plane-parallelflat-sky formalism for lensing reconstruction to account for a full-sky surveyusing the Spherical Fourier-Bessel (SFB) expansion. Using the HIRAX 21 cmsurvey as a basis, we make predictions for lensing-reconstruction noise in ourformalism and compare our results with the predictions from the plane-parallelformalism. We find agreement with the plane-parallel noise power spectrum atsmall scales and a significant deviation at scales $L\lesssim \ell_{\rmres}-k_{\rm eq}R$ where $R$ is the radius of the shell volume, $k_{\rm eq}$ isthe wavenumber for matter-radiation equality, and $\ell_{\rm res}$ is theangular resolution scale. Furthermore, we derive the SFB flat-skyreconstruction noise and compare it with the full-sky SFB case as well as theplane-parallel case, finding minor deviations from the full-sky noise due tosphericity. We also determine that, in the absence of non-Gaussian statisticsof the intensity field but accounting for foregrounds, the signal-to-noiseratio (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 becrucial for large-scale cosmology.

Full-Sky Lensing Reconstruction of 21 cm Intensity Maps