Detecting the 21 cm Signal of the Cosmic Dark Ages

The cosmic "Dark Ages" is the period between the last scattering of the Cosmic Microwave Background (CMB) and the appearance of the first luminous sources, spanning redshifts $1100\gtrsim z\gtrsim 30$. The only way to observe this period is by examining the 21 cm hyperfine transition line of neutral hydrogen HI, which -- given the high redshifts (and hence long wavelengths) -- must be observed from outside the Earth's ionosphere. Given the faintness of the signal, concepts for a radio array on the lunar far side (where large collecting areas can be deployed and radio frequency interference is minimal) have been proposed, like FarView or FARSIDE, but designs are still in the preliminary stages. This paper studies multiple aspects of array design to determine the impact of different design decisions on sensitivity to the Dark Ages 21 cm power spectrum. We do so by using the sensitivity package 21cmSense to model and simulate various array configurations. We present a fiducial design based on a modification of the FarView concept, which consists of a collecting area of $\sim2.5\,\rm{km}^{2}$ with 82,944 tightly packed dual-polarization dipoles grouped into 5,184 correlated elements, or subarrays, delivering a $>10\sigma$ detection of the $z=30$ signal with a five year lifetime. We find that, beyond mere collecting area, the most important factor in achieving this sensitivity is the presence of very short baselines that can only be realized with small, closely packed antennas.