Recovering lost 21 cm radial modes via cosmic tidal reconstruction
  21 cm intensity mapping has emerged as a promising technique to map the
large-scale structure of the Universe, at redshifts $z$ from 1 to 10.
Unfortunately, many of the key cross-correlations with the cosmic microwave
background and photo-$z$ galaxies have been thought to be impossible due to the
foreground contamination for radial modes with small wave numbers. In this
paper, we apply tidal reconstruction to the simulated 21 cm fields and recover
the lost large-scale radial modes successfully. We estimate the detectability
of the cross-correlation signals and find they can be detected at high
significance with current 21 cm experiments. The tidal field reconstruction
method opens up a new set of possibilities to probe the Universe and is
extremely valuable not only for 21 cm surveys but also for cosmic microwave
background and photometric-redshift observations.
