  We investigate the possibility to detect the integrated Sachs-Wolfe (ISW)
effect by cross-correlating 21-cm surveys at high redshifts with galaxies, in a
way similar to the usual CMB-galaxy cross-correlation. The high-redshift 21-cm
signal is dominated by CMB photons that travel freely without interacting with
the intervening matter, and hence its late-time ISW signature should correlate
extremely well with that of the CMB at its peak frequencies. Using the 21-cm
temperature brightness instead of the CMB would thus be a further check of the
detection of the ISW effect, measured by different instruments at different
frequencies and suffering from different systematics. We also study the ISW
effect on the photons that are scattered by HI clouds. We show that a detection
of the unscattered photons is achievable with planned radio arrays, while one
using scattered photons will require advanced radio interferometers, either an
extended version of the planned Square Kilometre Array or futuristic
experiments such as a lunar radio array.
