Precision measurement of cosmic magnification from 21-cm emitting galaxies

We show how precision lensing measurements can be obtained through the lensing magnification effect in high-redshift 21-cm emission from galaxies. Previously, cosmic magnification measurements have been seriously complicated by galaxy clustering. With precise redshifts obtained using the 21-cm emission line wavelength, one can correlate galaxies at different source planes, or exclude close pairs to eliminate such contamination. We provide forecasts for future surveys, specifically the Square Kilometer Array (SKA) and the Canadian Large Adaptive Reflector (CLAR). SKA can achieve similar to 1 per cent 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 increases the number of observed galaxies significantly, such that CLAR can also measure the dark-matter lensing power spectrum. SKA can also allow precise measurement of bispectrum lensing.