The Impact of Foregrounds on Dark Ages Measurements with the Highly Redshifted 21 cm Line

Studies of the cosmic dark ages ($30 \lesssim z \lesssim 150$) using the highly redshifted 21 cm line of neutral hydrogen offer unparalleled amounts of cosmological information, and recent years have seen the refinement of concepts for such experiments (e.g. CoDEX and FarView), nominally feasible with technology and resources in the next one to two decades. This work studies how the "foreground wedge" -- a term in the 21 cm cosmology literature referring to the contamination of power spectrum modes through the combination of smooth-spectrum foreground emission and the frequency-dependent point spread function of a radio interferometer -- manifests at these very high redshifts. We find the effect is more significant than at Epoch of Reionization redshifts targeted by current ground-based experiments, with foreground avoidance techniques (which discard all $k$ modes falling within the wedge) typically losing an order of magnitude of sensitivity. Given the extreme faintness of the 21 cm signal from the cosmic dark ages and the very high sky temperatures (the dominant source of noise) at low radio frequencies, we conclude that some level of foreground subtraction will be necessary to enable dark ages 21 cm cosmology with experiments of the scale believed to be achievable in the near term.