Mondal and Barkana (2023) quantified the idealized, thermal-noise-limited cosmological returns of dark-ages 21-cm observations: a global-signal measurement at 1,000 h integration would constrain a parameter combination to about 10%, and power-spectrum arrays with 10–100 km2^2 collecting area and long integrations could rival or beat Planck on the helium fraction (up to almost fifty times better in the largest configuration) and on the neutrino mass. These forecasts assume foregrounds are removed to below thermal noise — a part in 10610^{6} spectral-subtraction accuracy for the global signal — and treat the interferometric foreground wedge only roughly. The open problem is to replace this idealized baseline with a realistic, foreground- and instrument-limited answer: quantify the foreground subtraction and/or avoidance that is actually achievable for dark-ages (z≳30z\gtrsim 30) observations, determine the usable Fourier volume and residual contamination for realistic lunar/space instrument designs, and propagate these limits, together with the needed modeling refinements, into revised forecasts of the achievable cosmological precision. Recent work has sharpened but not resolved this: Pober and Smith (2025) showed that foreground avoidance alone loses about an order of magnitude in sensitivity at dark-ages redshifts, making some subtraction necessary, while the achievable subtraction accuracy remains unquantified.

Background

The cosmological 'dark ages' denote the period between photon decoupling (redshift z≈1100z\approx 1100) and the formation of the first luminous sources (z≈30z\approx 30). During this epoch the primordial neutral hydrogen gas emitted the 21-cm hyperfine-line radiation, redshifted today into frequencies below ∼50\sim 50 MHz. Two observables are distinguished: the global signal, the sky-averaged brightness temperature as a function of frequency, and the 21-cm power spectrum, the fluctuation signal as a function of scale and frequency. Because the relevant fluctuations were still in the linear regime and uncontaminated by astrophysical sources, these observables carry exceptionally clean cosmological information (the ground-based ionosphere and radio-frequency interference block the band from Earth, so dark-ages measurements require lunar or space-based instruments such as LuSEE-Night, FarView, CosmoCube, or CoDEX). Mondal and Barkana (2023) used Fisher-matrix forecasts (a linearized covariance method mapping experimental noise to parameter errors) with thermal noise plus cosmic variance to show that, in the best configurations considered (collecting areas of 10–100 km2^2 — a 10 km2^2 array already corresponds to of order 400,000 antenna stations — and integration times up to 100,000 h), the 21-cm signal could constrain combinations of Λ\LambdaCDM (the standard cold-dark-matter cosmology) parameters to sub-percent precision, measure the cosmic helium fraction up to almost fifty times better than Planck, and match or beat Planck on the neutrino mass. The catch is astrophysical foregrounds: Galactic synchrotron emission is of order 10410^{4} K brightness at these frequencies, roughly seven orders of magnitude brighter than the millikelvin cosmological signal, so residual foregrounds must be suppressed below the thermal noise for these forecasts to apply. For the global signal, Mondal and Barkana note this requires spectral-subtraction accuracy at the level of a part in 10610^{6} for a 1,000 h integration. For the power spectrum, the alternative to subtraction is avoidance: smooth-spectrum foregrounds leak predominantly into a 'wedge'-shaped region of the (k⊥,k∥)(k_{\perp},k_{\parallel}) Fourier plane (the wavevector components perpendicular and parallel to the line of sight) through the frequency dependence of an interferometer's response, so one can discard wedge modes and analyze the rest; Mondal and Barkana estimated this loss only roughly, with an effective contamination angle θL\theta_{\mathrm{L}} bracketed between an optimistic and a pessimistic value, and presented their thermal-noise-limited results as a benchmark for experiments which face additional practical challenges including foreground removal. Their analysis also deliberately smoothed the theoretical signal but not the noise power spectrum (a conservative approximation), used linear theory for the 21-cm signal (later work showed that small-scale dark-matter clumping and the separate evolution of baryons versus cold dark matter measurably modify the dark-ages signal), and fixed the fiducial thermal history against possible contamination by early galaxies at zz up to ∼35\sim 35. Together these choices define the gap the problem targets: the published baseline is an ideal thermal-noise-limited bound, while the realistic, foreground-limited precision of dark-ages 21-cm cosmology is unknown.

Problem Statement

Determine the realistic, foreground- and instrument-limited prospects for precision cosmology with the dark-ages 21-cm signal, replacing the idealized thermal-noise-limited baseline of Mondal and Barkana (2023). Concretely, an answer must: (1) quantify the accuracy of foreground subtraction achievable for dark-ages observations — for the global signal, whether residual foregrounds can be driven below the thermal noise (a part in 10610^{6} in spectral accuracy at tint=1,000t_{\mathrm{int}}=1{,}000 h) under realistic lunar/space observing conditions, and for the power spectrum, the residual contamination achievable outside the foreground wedge; (2) characterize the effective foreground-avoidance loss for realistic instrument designs — including the Mondal and Barkana (2023) configurations with 10–100 km2^2 collecting area — i.e. the effective contamination angle θL\theta_{\mathrm{L}} and the resulting usable (k⊥,k∥)(k_{\perp},k_{\parallel}) mode volume, beyond the rough optimistic/pessimistic bracketing in the source; and (3) propagate these foreground limits into revised forecasts of the achievable precision on the cosmological quantities at stake — the Λ\LambdaCDM parameter combinations, the primordial helium fraction, and the neutrino mass — stating how much of the idealized forecast precision survives realistic foreground treatment, and taking into account the identified modeling refinements (consistent angular smoothing of signal and noise, non-linear corrections such as small-scale clumping and baryon–CDM separation, and astrophysical-uncertainty nuisance treatment) to the extent that they affect the achievable precision.

References

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