We show how precision lensing measurements can be obtained through the
lensing magnification effect in high redshift 21cm emission from galaxies.
Normally, cosmic magnification measurements have been seriously complicated by
galaxy clustering. With precise redshifts obtained from 21cm emission line
wavelength, one can correlate galaxies at different source planes, or exclude
close pairs to eliminate such contaminations.
We provide forecasts for future surveys, specifically the SKA and CLAR. SKA
can achieve percent precision on the dark matter power spectrum and the galaxy
dark matter cross correlation power spectrum, while CLAR can measure an
accurate cross correlation power spectrum. The neutral hydrogen fraction was
most likely significantly higher at high redshifts, which improves the number
of observed galaxies significantly, such that also CLAR can measure the dark
matter lensing power spectrum. SKA can also allow precise measurement of
lensing bispectrum.Comment: 11 pages, 8 figures. Accepted to MNRAS. We deleted two figures and
shortened the paper to meet MNRAS's requirement. All main results remain
unchange