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

TL;DR

This paper investigates how weak gravitational lensing affects the 3D 21-cm radiation background, proposing methods to reconstruct the lensing field and emphasizing the importance of high-resolution observations for detection.

Contribution

It introduces a detailed formalism for 3D weak lensing of the 21-cm background, including covariance analysis and quadratic estimators for lensing reconstruction.

Findings

Lensing correlates different multipoles, breaking statistical homogeneity.

Measurement effects significantly impact covariance off-diagonal terms.

Detection of lensing requires high-resolution, sensitive observations with future radio arrays.

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 $C_{\ell}(k,k')$ 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 $\hat{\phi}_{\ell m}(\kappa)$ 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 $C_{\ell}(k,k')$. 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.