Modes of the Dark Ages 21 cm field accessible to a lunar radio interferometer

At redshifts beyond z greater than or similar to 30, the 21 cm line from neutral hydrogen is expected to be essentially the only viable probe of the three-dimensional matter distribution. The lunar far-side is an extremely appealing site for future radio arrays that target this signal, as it is protected from terrestrial radio frequency interference, and has no ionosphere to attenuate and absorb radio emission at low frequencies (tens of MHz and below). We forecast the sensitivity of low-frequency lunar radio arrays to the bispectrum of the 21 cm brightness temperature field, which can in turn be used to probe primordial non-Gaussianity generated by particular early universe models. We account for the loss of particular regions of Fourier space due to instrumental limitations and systematic effects, and predict the sensitivity of different representative array designs to local-type non-Gaussianity in the bispectrum, parametrized by fNL. Under the most optimistic assumption of sample variance-limited observations, we find that sigma(fNL)less than or similar to 0.01 could be achieved for several broad redshift bins at z greater than or similar to 30 if foregrounds can be removed effectively. These values degrade to between sigma(fNL)similar to 0.03 and 0.7 for z=30 to z=170, respectively, when a large foreground wedge region is excluded.This article is part of a discussion meeting issue 'Astronomy from the Moon: the next decades (part 2)'.