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The current upper limit on the tensor-to-scalar ratio r is ~0.2, and should improve by an order of magnitude with future experiments. These authors claim that measuring the curl component of the lensing power spectrum of 21cm emission could yield incredible constraints r~10^(-9) (though this headline figure corresponds to their most optimistic case). The angular resolution of our planned 21cm telescopes is the crucial quantity in determining these constraints.

This is a very thought-provoking paper. At z=50 - the redshifted wavelength of HI is 21 cm * 51 which is 21m [about the length of a cricket wicket]. To image fluctuations you would need to space antennae by about half a wavelength, or by ~10 m. So far, so good, LOFAR is trying this already, filling many cricket pitches worth of land with antennae in Northern Holland. The UK even has its own little version at Chilbolton near Winchester. So far, so good. However, to get to r~10^-9 you need (apparently) to get to l_ max ~ 10^7, or an angular resolution of about 0.01 arcsec (Better than Hubble Space Telescope resolution). This means that, according to lambda/D, the total size of your 21-cm instrument has to have a diameter of ~ [21 m] / (10^-7), or ~10-times larger than the Earth. Of course, the atmosphere is getting close to opaque at these wavelengths, and the radio frequency interference is so bad that you'd want to put such an instrument on the back side of the moon. Unfortunately, the moon isn't large enough either, so you'd have to launch (or remotely deploy) something ~10-times the size of the Earth into deep space. This might be quite expensive, but in the SKA project we have most of the machinery to simulate such an instrument if any of you theorists out there are interested in collaboration.