A complete uncertainty budget for the dark-ages global 21-cm signal prediction: current datasets, recombination modelling, beyond-$\Lambda$CDM extensions, and lunar-mission forecasts

The dark-ages global 21-cm signal — the sky-averaged hydrogen hyperfine-line brightness temperature between recombination ($z\approx 1100$) and the first stars ($z\approx 30$) — is a nearly astrophysics-free consequence of the standard cosmological model $\Lambda$CDM. Bevins (2026) propagated $\Lambda$CDM constraints from Planck, the WMAP satellite, baryon acoustic oscillations, and the Dark Energy Survey (DES) Year 1 through an analytic signal model, finding that within $\Lambda$CDM the absorption depth from the Planck chains is pinned to about $-44.09\pm 0.96$ mK at a central frequency of $17.14\pm 0.03$ MHz, but left open the four ingredients needed for a complete, mission-ready prediction: the impact of newer datasets (from the Atacama Cosmology Telescope, ACT; the Dark Energy Spectroscopic Instrument, DESI; updated DES releases; and Type Ia supernova compilations), the treatment of recombination-code modelling choices (HYREC-2 versus recfast++, two recombination-history codes) as a theoretical uncertainty, the propagation of beyond-$\Lambda$CDM parameter posteriors, and end-to-end forecasts combining the cosmology-driven signal posterior with realistic instrument and foreground models. The problem is to establish the dark-ages $T_{21}(\nu)$ prediction with a complete uncertainty budget and to convert it into quantitative observational requirements for lunar experiments.

Background

Between the release of the cosmic microwave background (CMB — the relic radiation that decoupled from matter at redshift $z\approx 1100$) and the formation of the first luminous sources around $z\approx 30$ lies the largely unobserved "dark ages". The universe then contained no stars or galaxies, only neutral hydrogen gas, and its cleanest predicted observable is the global 21-cm signal: the sky-averaged brightness temperature of the 21-cm hyperfine emission line of neutral hydrogen, measured relative to the radio background and observed as a function of frequency $\nu$ (equivalently redshift). The signal $T_{21}(\nu)$ is set by well-understood atomic and cosmological physics. The spin temperature $T_s$ — the effective excitation temperature of the hydrogen hyperfine transition — is coupled to the kinetic gas temperature $T_k$ by collisions between hydrogen atoms during this epoch, with a coupling efficiency that grows with gas density; the gas thermally decouples from the CMB and then cools adiabatically, so $T_k$ falls below the radiation temperature and the line appears in absorption. Because no astrophysical sources operate yet, $T_{21}(\nu)$ during the dark ages follows almost parameter-free from $\Lambda$CDM (the standard cosmological model of cold dark matter plus a cosmological constant) through a handful of parameters: the present-day expansion rate $H_0$, the matter and baryon density parameters $\Omega_m$ and $\Omega_b$, and the primordial helium abundance $Y_{\rm He}$. The required recombination history — the free-electron fraction $x_e(z)$ and gas temperature $T_k(z)$ — is computed with codes such as HYREC-2 (a multilevel-atom recombination code treating radiative transfer) and recfast++ (a fast code based on an effective three-level atom), which agree closely but not exactly.

Bevins (2026) took the publicly released Markov-chain Monte Carlo (MCMC) chains constraining $\Lambda$CDM from four probes — the Planck 2018 and WMAP (Wilkinson Microwave Anisotropy Probe) 9-year CMB analyses, combined baryon acoustic oscillation (BAO) measurements from galaxy surveys, and DES Year-1 galaxy clustering and lensing (DES being the Dark Energy Survey) — and propagated them through an analytic dark-ages signal model, obtaining functional posteriors on $T_{21}(\nu)$ over $z=30$–$1100$. Within the modelling assumptions and $\Lambda$CDM, the Planck chains imply an absorption trough of depth $-44.09\pm 0.96$ mK centred at $17.14\pm 0.03$ MHz; differences between the HYREC-2 and recfast++ recombination histories are well below this $\Lambda$CDM-parameter-driven uncertainty. The derived observational implications are severe: to be competitive with Planck, a dark-ages experiment must calibrate to better than roughly 1 mK, against astrophysical foregrounds (dominated by Galactic synchrotron emission) of order $10^5$ K at these frequencies. Observing the signal at all requires getting above the ionosphere, which attenuates the sky below about 40 MHz — motivating lunar far-side mission concepts such as CosmoCube, FarView, and the Lunar Crater Radio Telescope. The scientific stakes are high: the absorption feature reported by the EDGES experiment (Experiment to Detect the Global Epoch of Reionization Signature; Bowman et al. 2018) is anomalously deep if cosmological, and the Hubble tension — the discrepancy between early- and late-universe measurements of $H_0$ — shows that early- and late-time probes are not fully consistent; a dark-ages detection would test the many beyond-$\Lambda$CDM explanations proposed for both, including exotic energy injection, dark-matter–baryon interactions, and additional radio backgrounds. Precision-cosmology forecasts (e.g. Mondal & Barkana 2023) show the dark-ages signal could ultimately constrain cosmology better than the CMB, and codes such as 21cmFirstCLASS (Flitter & Kovetz 2024) already compute the global signal for $\Lambda$CDM and extensions — which makes quantifying how well the signal is currently predicted, and how uncertain that prediction is, a well-posed and timely question.

Problem Statement

Determine how well the dark-ages global 21-cm signal — the sky-averaged brightness temperature $T_{21}(\nu)$ of the 21-cm hydrogen hyperfine line between recombination ($z\approx 1100$) and the first stars ($z\approx 30$), as a function of frequency $\nu$ — is predicted given all current cosmological knowledge, and what a lunar experiment must achieve to test that prediction. The baseline prediction of Bevins (2026) — within $\Lambda$CDM (the standard cosmological model), an absorption trough of depth $-44.09\pm 0.96$ mK at $17.14\pm 0.03$ MHz from the Planck chains, alongside the propagated WMAP, BAO, and DES Year-1 posteriors — must be completed along four linked components that together constitute the full uncertainty budget and its observational translation:

(i) Dataset completeness. Propagate the current early- and late-time $\Lambda$CDM constraints — ACT (Atacama Cosmology Telescope) CMB data, DESI (Dark Energy Spectroscopic Instrument) BAO measurements, updated DES releases, and Type Ia supernova compilations (e.g. Pantheon+, SH0ES, DES5Y) — through the dark-ages signal model, quantifying how the propagated $T_{21}(\nu)$ posterior (depth, central frequency, and full spectral shape) tightens or shifts relative to the Planck/WMAP/BAO/DES-Y1 baseline, with the mild inter-catalogue tensions treated in a statistically principled way.

(ii) Theoretical error. Quantify the modelling-choice uncertainty from the recombination and thermal history — currently the difference between the HYREC-2 and recfast++ recombination codes, subdominant and well below the ~1 mK $\Lambda$CDM-parameter-driven uncertainty — as a contribution to the reported $T_{21}(\nu)$ posterior.

(iii) Beyond-standard-model generality. Extend the propagation beyond standard $\Lambda$CDM to its well-motivated alternatives — exotic energy injection, dark-matter–baryon interactions, and additional radio backgrounds — propagating those models' existing parameter posteriors into their predicted dark-ages signals, so the $\Lambda$CDM prediction is positioned against them.

(iv) End-to-end mission translation. Combine the resulting cosmology-driven $T_{21}(\nu)$ posterior with realistic instrument-calibration and astrophysical-foreground models to produce end-to-end forecasts for lunar dark-ages experiments, translating the prediction into quantitative mission requirements (target frequency band, calibration precision, frequency coverage, integration time).

The common objective uniting these components is a single defensible prediction of the dark-ages 21-cm signal with a complete, quantified uncertainty budget — spanning data, theory, and model class — and its conversion into observational requirements; components (i)–(iii) supply the three uncertainty sources of the prediction, and component (iv) consumes them. The resulting prediction states what the dark-ages signal should look like — $T_{21}(\nu)$ with a complete, quantified uncertainty budget spanning data, theory, and model class — and how precisely a lunar experiment must measure it.

References

1. Bevins, Harry T. J. (2026). The Magnitude of the Dark Ages 21 cm Signal in the Context of Existing Early and Late Time Constraints on ΛCDM. The Astrophysical Journal Letters 997, L35. DOI: 10.3847/2041-8213/ae356b. https://doi.org/10.3847/2041-8213/ae356b (arXiv:2512.11568, https://arxiv.org/abs/2512.11568)
2. Yoshiura, Shintaro; Okamatsu, Fumiya; Takahashi, Tomo (2026). Detectability and Template Distinguishability of the Dark Ages 21 cm Global Signal with Wide and Sparse Frequency Coverage. arXiv:2602.01263. https://arxiv.org/abs/2602.01263
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7. Pober, Jonathan C.; Smith, Willow (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
8. Mondal, Rajesh; Barkana, Rennan (2023). Prospects for precision cosmology with the 21 cm signal from the dark ages. Nature Astronomy 7, 1025–1030. DOI: 10.1038/s41550-023-02057-y. https://doi.org/10.1038/s41550-023-02057-y
9. Mondal, Rajesh; Barkana, Rennan; Fialkov, Anastasia (2023). Constraining exotic dark matter models with the dark ages 21-cm signal. Monthly Notices of the Royal Astronomical Society 527, 1461–1471. DOI: 10.1093/mnras/stad3317. https://doi.org/10.1093/mnras/stad3317
10. Slatyer, Tracy R.; Wu, Chih-Liang (2018). Early-Universe constraints on dark matter-baryon scattering and their implications for a global 21 cm signal. Physical Review D 98, 023013. DOI: 10.1103/PhysRevD.98.023013. https://doi.org/10.1103/PhysRevD.98.023013
11. Flitter, Jordan; Kovetz, Ely D. (2024). New tool for 21-cm cosmology. I. Probing ΛCDM and beyond. Physical Review D 109, 043512. DOI: 10.1103/PhysRevD.109.043512. https://doi.org/10.1103/PhysRevD.109.043512 (the code is named 21cmFirstCLASS; the preprint, arXiv:2309.03942, https://arxiv.org/abs/2309.03942, is titled '21cmFirstCLASS I. Cosmological tool for ΛCDM and beyond')