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

At redshifts beyond $z \gtrsim 30$, the 21cm line from neutral hydrogen is expected to be essentially the only viable probe of the 3D 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 21cm 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, parametrised by $f_{\rm NL}$. Under the most optimistic assumption of sample variance-limited observations, we find that $\sigma(f_{\rm NL}) \lesssim 0.01$ could be achieved for several broad redshift bins at $z \gtrsim 30$ if foregrounds can be removed effectively. These values degrade to between $\sigma(f_{\rm NL}) \sim 0.03$ and $0.7$ for $z=30$ to $z=170$ respectively when a large foreground wedge region is excluded.