Detectability and Model Discriminability of the Dark Ages 21 cm Global Signal

The 21 cm signal from neutral hydrogen atom is almost the only way to directly probe the Dark Ages. The Dark Ages 21 cm signal, observed at frequencies below 50 MHz, can serve as a powerful probe of cosmology, as the standard cosmological model predicts a well-defined 21 cm spectral shape. In this work, we assess the detectability and model-selection power of 21 cm observations assuming physically motivated foregrounds, optimistic error levels, and several observing strategies for the signals predicted in various cosmological models. Using a Bayesian evidence-based comparison, we find that wide-band observations covering 1-50 MHz can identify the evidence of non-zero 21 cm signals from models considered in this paper except the one with a smooth spectrum that peaks at lower frequencies. In particular, observations below 15 MHz are essential to avoid degeneracies with the foreground. Furthermore, even with observations measured at 5 MHz intervals over the frequency range 1-50 MHz, the 21 cm signal can be identified if the errors are sufficiently small. This indicates that the intrinsic 21 cm spectral shape can be captured without foreground degeneracy even with a limited number of frequency channels.

💡 Research Summary

This paper investigates the detectability and model‑selection power of the global 21 cm signal from the Dark Ages (frequencies < 50 MHz) using a Bayesian evidence framework. Eight cosmological scenarios are considered: the standard ΛCDM absorption trough, two dark‑matter–baryon coupling models (weak and strong), an early‑dark‑energy model, an excess radio background model, a light‑dark‑matter decay model, two primordial‑magnetic‑field heating models (one producing a shallow absorption, the other an emission feature), and a null‑signal case. The 21 cm spectra are generated with a modified RECFast code, while the foreground is modeled physically as a combination of Galactic synchrotron emission and free‑free absorption, with parameters anchored to observational data (e.g., T_G≈2.45×10⁵ K, spectral index α≈0.515).

Three observing strategies are examined: (1) continuous coverage from 1 MHz to 50 MHz with 1 MHz channels (wide‑band antenna), (2) the same frequency range sampled at 5 MHz intervals using separate, optimized antennas for each channel, and (3) continuous coverage from 15 MHz to 50 MHz only. Instrumental noise is assumed to be the sum of sky temperature and a receiver temperature up to 3000 K; a fiducial per‑channel noise floor of 5 mK is adopted because it yields a “very strong” Bayesian detection (Δln Z > 5) for the ΛCDM model.

Evidence values (ln Z) are computed with PolyChord nested sampling. Model i is deemed detectable if Δln Z_i,0 = ln Z_i − ln Z_0 > 1, where Z_0 corresponds to the null‑signal model. The interpretation follows Kass & Raftery: 1–3 = positive, 3–5 = strong, >5 = very strong. Results show that with strategy (1) and 5 mK noise, ΛCDM, the two DM‑baryon coupling models, early‑dark‑energy, light‑dark‑matter decay, and the weak‑magnetic‑field heating model all achieve Δln Z > 3 (strong detection). The excess‑radio‑background model reaches Δln Z≈2.4 (positive), while the emission‑type magnetic‑field model (PMFs) yields Δln Z≈‑0.3, indicating it is completely absorbed by the foreground and remains undetectable. Raising the noise to 100 mK eliminates strong evidence for all models, underscoring the need for sub‑10 mK systematics.

Strategy (2), despite using only eight frequency points, still recovers strong evidence for the same set of models provided the noise remains ≤5 mK, demonstrating that a sparse frequency sampling can suffice if each channel is well‑calibrated and the foreground is accurately modeled. Strategy (3) (cutting off below 15 MHz) loses discriminating power because low‑frequency data are crucial for breaking degeneracies between foreground curvature and signal shape; without them, some models become indistinguishable from foreground variations.

The analysis highlights two practical implications. First, low‑frequency (< 15 MHz) observations are essential because the foreground rises steeply (∝ ν⁻²·⁵) and can otherwise mask subtle spectral features. Second, models that produce an emission feature (PMFs) are intrinsically hard to detect with the assumed foreground because the foreground model can absorb the signal’s shape; detecting such cases would require either a broader frequency band (e.g., extending below 1 MHz) or independent constraints on foreground parameters from ancillary surveys.

In summary, under optimistic but realistic assumptions—physically motivated foreground modeling, a per‑channel noise floor of ≤5 mK, and well‑designed observing strategies—the global 21 cm signal from the Dark Ages can be detected with very strong Bayesian evidence, and a range of non‑standard cosmologies can be distinguished from ΛCDM. However, successful detection of models whose spectral signatures overlap strongly with foreground curvature (e.g., emission‑type signals) will demand more aggressive instrument designs, tighter foreground priors, or complementary observations.