Full-Sky Lensing Reconstruction of 21 cm Intensity Maps

Abstract

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 $L\lesssim {\ell }_{\mathrm{res}}-k_{\mathrm{eq}}R$ where $R$ is the radius of the shell volume, $k_{\mathrm{eq}}$ is the wavenumber for matter-radiation equality, and ${\ell }_{\mathrm{res}}$ 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 $C_{\ell }^{\varphi \varphi }$ 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.

arXiv comment19 pages, 9 figures, submitted to MNRAS

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• A new probe of the high-redshift Universe: nulling CMB lensing with interloper-free "LIM-pair" lensing
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• A Differentiable, End-to-End Forward Model for 21 cm Cosmology: Estimating the Foreground, Instrument, and Signal Joint Posterior
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