Title: Simulations for 21 cm radiation lensing at EoR redshifts,
Abstract: We introduce simulations aimed at assessing how well weak gravitational
lensing of 21cm radiation from the Epoch of Reionization ($z \sim 8$) can be
measured by an SKA-like radio telescope. A simulation pipeline has been
implemented to study the performance of lensing reconstruction techniques. We
show how well the lensing signal can be reconstructed using the
three-dimensional quadratic lensing estimator in Fourier space assuming
different survey strategies. The numerical code introduced in this work is
capable of dealing with issues that can not be treated analytically such as the
discreteness of visibility measurements and the inclusion of a realistic model
for the antennae distribution. This paves the way for future numerical studies
implementing more realistic reionization models, foreground subtraction
schemes, and testing the performance of lensing estimators that take into
account the non-Gaussian distribution of HI after reionization. If multiple
frequency channels covering $z \sim 7-11.6$ are combined, Phase 1 of SKA-Low
should be able to obtain good quality images of the lensing potential with a
total resolution of $\sim 1.6$ arcmin. The SKA-Low Phase 2 should be capable of
providing images with high-fidelity even using data from $z\sim 7.7 - 8.3$. We
perform tests aimed at evaluating the numerical implementation of the mapping
reconstruction. We also discuss the possibility of measuring an accurate
lensing power spectrum. Combining data from $z \sim 7-11.6$ using the SKA2-Low
telescope model, we find constraints comparable to sample variance in the range
$L<1000$, even for survey areas as small as $25\mbox{ deg}^2$.