Three-dimensional weak gravitational lensing of the 21-cm radiation background

Abstract

ABSTRACT We study weak gravitational lensing by the cosmic large-scale structure of the 21-cm radiation background in the 3D weak-lensing formalism. The interplay between source distance measured at finite resolution, visibility, and lensing terms is analysed in detail and the resulting total covariance Cℓ(k, k′) is derived. The effect of lensing correlates different multipoles through convolution, breaking the statistical homogeneity of the 21-cm radiation background. This homogeneity breaking can be exploited to reconstruct the lensing field $\hat{\phi }_{\rm \ell m}(\kappa)$ and noise-lensing reconstruction $N_{\ell }^{\hat{\phi }}$ by means of quadratic estimators. The effects related to the actual measurement process (redshift precision and visibility terms) change drastically the values of the off-diagonal terms of the total covariance Cℓ(k, k′). It is expected that the detection of lensing effects on a 21-cm radiation background will require sensitive studies and high-resolution observations by future low-frequency radio arrays such as the SKA survey.