Pober & Smith (2025) showed that the 'foreground wedge' — the loss of Fourier modes caused by spectrally smooth radio foregrounds leaking through the frequency-dependent response of an interferometer — removes roughly an order of magnitude in detection significance for a future lunar-farside measurement of the 21 cm signal from the cosmic dark ages (30≲z≲15030 \lesssim z \lesssim 150), so foreground avoidance alone cannot enable dark-ages cosmology with near-term-scale arrays and some level of foreground subtraction is required. They explicitly left open the problem of converting this finding into definitive experimental requirements and detection forecasts, which the Problem Statement below states in full.

Background

The cosmic dark ages (30≲z≲15030 \lesssim z \lesssim 150) are the period between the release of the cosmic microwave background and the formation of the first luminous sources; the only anticipated way to map structure then is the 21 cm hyperfine emission line of neutral hydrogen, redshifted to frequencies of roughly 10–45 MHz. These frequencies are blocked by the Earth's ionosphere, so experiments (such as the proposed lunar-farside arrays FarView and DEX) must operate from space or the Moon. The signal is extremely faint and the foreground emission — dominated by Galactic synchrotron radiation — is about five orders of magnitude brighter. Interferometric 21 cm measurements are usually summarized as a power spectrum in cosmological Fourier space, with k⊥k_\perp and k∥k_\parallel the wavenumbers across and along the line of sight. Because an interferometer's point-spread function changes with frequency ('chromaticity'), spectrally smooth foregrounds are smeared into a region of this Fourier space called the 'foreground wedge', whose slope steepens with redshift; at dark-ages redshifts the wedge occupies roughly 90% of the two-dimensional kk-space. Two mitigation strategies exist: foreground avoidance, which simply discards all modes inside the wedge (the approach of most current ground-based Epoch-of-Reionization (EoR) experiments), and foreground subtraction, which attempts to model and remove the foreground emission so that some wedge modes can be used. Pober & Smith (2025, arXiv:2507.22993) analyzed how the wedge affects dark-ages measurements, using the sensitivity-forecasting code 21cmSense and the fiducial lunar array of Smith & Pober (2025, arXiv:2504.08965), a ‘∼‘`\sim`2.5 km2^2 compact array of ‘∼‘`\sim`83,000 dipoles grouped into correlated subarrays that yields a 10σ\sigma detection of the z=30z = 30 power spectrum in five years in the absence of foregrounds. They found that avoiding the wedge costs approximately a factor of ten in detection significance; recovering it would require about 50 years of observing or a ‘∼‘`\sim`25 km2^2 array. They therefore concluded that foreground subtraction is likely a requirement for dark-ages cosmology with experiments achievable in the next one to two decades. However, their forecast rests on simplifications they explicitly flag: foregrounds are treated only as a best-case wedge cut with no demonstrated subtraction algorithm and no mapping from subtraction techniques to recoverable modes; sensitivities use an 18 MHz bandwidth approximation without forward-modeling the mixing of signal from overlapping redshift bins (a nearly co-eval bin at these redshifts spans Δz≲0.5\Delta z \lesssim 0.5); sample variance — the cosmic variance that dominates once thermal noise is reduced — is excluded, so only aggregate detection significance, not cosmological-parameter constraints, is forecast; the sky noise is modeled as a pure Galactic synchrotron power law, which may overestimate system temperatures where the Galactic plane becomes optically thick to low-frequency radiation due to free-free absorption by ionized gas; the benefits of operating above the ionosphere in a radio-quiet lunar environment are noted but not quantified; and the exact wedge shape is known to depend on the power-spectrum estimator and array layout, which the analysis holds fixed. These gaps jointly define what remains to be done.

Problem Statement

Convert the wedge-geometry and sensitivity findings of Pober & Smith (2025) into definitive experimental requirements and detection forecasts for dark-ages 21 cm cosmology. This jointly requires: (1) developing and demonstrating foreground-subtraction algorithms tailored to the dark-ages regime — including realistic instrument chromaticity and beam sidelobe responses — and quantifying the fraction of foreground-wedge Fourier modes that can be reliably recovered by subtraction; (2) forward-modeling the redshift evolution of the 21 cm signal across overlapping, nearly co-eval redshift bins (Δz≲0.5\Delta z \lesssim 0.5) through the analysis, replacing the 18 MHz flat-band approximation; (3) incorporating sample variance and its interaction with foreground excision/subtraction so forecasts yield actual cosmological-parameter constraints rather than aggregate detection significance; (4) refining low-frequency sky-noise models by quantifying free-free absorption and Galactic-plane opacity at the relevant frequencies and their trade-off against lost lines of sight behind optically thick regions; (5) assessing how lunar- or space-based operating environments (absence of the ionosphere, different radio-frequency interference (RFI) and scattering environments) change achievable subtraction performance and hence the balance between avoidance and subtraction; and (6) mapping how concrete choices of power-spectrum estimator and array layout (including correlator/subarray architectures) modify the wedge footprint beyond horizon-limited estimates. The forecast is to be end-to-end and reproducible, using these ingredients to state what experiment scale, environment, and analysis strategy makes dark-ages (30≲z≲15030 \lesssim z \lesssim 150) 21 cm cosmology achievable, with detection significances and parameter constraints for named array concepts. The forecast is to address all six components above; a component that is physically negligible for this objective is to be argued as such within the analysis itself.

References

  1. Jonathan C. Pober & Willow Smith (2025), 'The Impact of Foregrounds on Dark Ages Measurements with the Highly Redshifted 21 cm Line', arXiv:2507.22993, https://arxiv.org/abs/2507.22993
  2. Willow Smith & Jonathan C. Pober (2025), 'Detecting the 21 cm Signal of the Cosmic Dark Ages', arXiv:2504.08965, https://arxiv.org/abs/2504.08965
  3. Willow Smith, Jonathan C. Pober, Bang D. Nahn, Jack O. Burns, Ronald S. Polidan (2026), 'Quantifying Foreground Contamination in the Dark Ages 21 cm Power Spectrum Using an Electromagnetically Simulated Dipole Antenna Atop a Dielectric Surface', arXiv:2607.11929, https://arxiv.org/abs/2607.11929
  4. Chen Zhang, Furen Deng, Yidong Xu, Bin Yue, Yuewei Wen, Xuelei Chen (2026), 'Wedge-avoidance Fisher Forecasts for Primordial Non-Gaussianity from Dark-Ages 21-cm Power Spectrum and Bispectrum', arXiv:2606.23314, https://arxiv.org/abs/2606.23314
  5. Yuewei Wen, Bin Yue, Yidong Xu, Furen Deng, Chen Zhang, Fengquan Wu, Xuelei Chen (2026), 'A Designer's Guide to Lunar Far-Side Interferometer Array: Power Spectrum Measurement and Cosmological Constraints from the Dark Ages', arXiv:2605.29276, https://arxiv.org/abs/2605.29276
  6. Jack O. Burns, Judd Bowman, Tzu-Ching Chang, Gregg Hallinan, Alex Hegedus, Nivedita Mahesh, Bang Nhan, Jonathan Pober, Ronald Polidan, Willow Smith, Nithyanandan Thyagarajan (2026), 'The FarView Low Frequency Radio Array on the Moon's Far Side: Science and Array Architecture', arXiv:2601.16170, https://arxiv.org/abs/2601.16170
  7. S. Ghosh, L. V. E. Koopmans, C. Brinkerink, A. R. Offringa, A. J. Boonstra, S. A. Brackenhoff, E. Ceccotti, J. K. Chege, L. Y. Gao, B. K. Gehlot, L. I. Gurvits, C. Höfer, F. G. Mertens, M. Mevius, S. Munshi, A. Saxena, J. A. Tauber, H. Vedantham, S. Yatawatta, S. Zaroubi (2025), 'The impact of lunar topography on the 21-cm power spectrum for grid-based arrays: Insights for the Dark-ages EXplorer (DEX)', arXiv:2512.08906, https://arxiv.org/abs/2512.08906