21-cm Signal Overview

Updated 22 February 2026

The 21‑cm signal is a redshifted hyperfine transition of neutral hydrogen that encodes the universe’s thermal, ionization, and density history across cosmic epochs.
It enables three-dimensional mapping of early structure formation, shedding light on star formation, dark matter properties, and exotic energy injections.
Advanced analytical and experimental techniques, including global signal recovery and power spectrum analysis, are crucial to overcome foreground and calibration challenges.

The 21-cm signal refers to the redshifted emission or absorption of the 21-cm hyperfine transition line of neutral hydrogen (H I) in the early universe. This signal encodes the thermal, ionization, and density history of the intergalactic medium (IGM) across a vast range of cosmic epochs—from recombination through the Dark Ages, Cosmic Dawn, and the Epoch of Reionization. As a three-dimensional tomographic probe, the 21-cm signal allows mapping of the structure formation process, the properties of the first sources of light, and potentially even exotic energy injections or cosmological parameters beyond the reach of the CMB and galaxy surveys.

1. Physical Origin and Formalism

The 21-cm line is caused by the hyperfine splitting of the hydrogen ground state, with a rest-frame frequency of 1420.4 MHz (wavelength 21.1 cm). The observable quantity is the differential brightness temperature, δT_b, relative to the cosmic microwave background (CMB), given by

$\delta T_b(z) \simeq 27\,\text{mK}\ x_{\rm HI}(1+\delta_b) \Bigl(\frac{\Omega_b h^2}{0.023}\Bigr) \Bigl(\frac{0.15}{\Omega_m h^2}\Bigr)^{1/2} \Bigl(\frac{1+z}{10}\Bigr)^{1/2} \Bigl[1 - \frac{T_{\rm CMB}(z)}{T_s(z)}\Bigr]$

where:

$x_{\rm HI}$ is the local neutral fraction,
$\delta_b$ is the baryonic overdensity,
$T_s$ is the spin temperature, governing the excitation of the hyperfine states,
$T_{\rm CMB}(z) = 2.725(1+z)$  K is the CMB temperature (Fialkov et al., 2013, Fialkov et al., 2023).

Key coupling mechanisms for $T_s$ are:

Collisional coupling: Efficient at high densities (Dark Ages), driving $T_s \to T_K$ , with $T_K$ the kinetic temperature.
Wouthuysen–Field effect: Lyα photon scattering mixes the hyperfine levels, coupling $T_s$ to the color temperature of the Lyα field, usually tracking $T_K$ .
In radiative equilibrium ( $T_s = T_{\rm CMB}$ ) the signal vanishes; nonzero $\delta T_b$ arises when $T_s \neq T_{\rm CMB}$ .

Global signal and fluctuations can be written, in the optically thin limit, as

$\delta T_b(\nu) = \frac{T_s(z) - T_\gamma(z)}{1+z} \tau_{21}(z)$

with

$\tau_{21}(z) = \frac{3 c \lambda_{21}^2 A_{10} n_{\rm HI}}{32\pi k_B T_s H(z)}$

where $\lambda_{21}$ is the 21-cm wavelength, $A_{10}$ the Einstein coefficient, and $n_{\rm HI}$ the hydrogen density (Fialkov et al., 2013).

2. Cosmic Epochs: Recombination, Dark Ages, Cosmic Dawn, and Reionization

2.1. Recombination and Dark Ages (z ≳ 30)

During and after recombination (z ≈ 500–1100), atomic collisions and the excess Lyα radiation field from recombinations cause $T_s$ to deviate from $T_{\rm CMB}$ by order unity, resulting in a global brightness contrast of up to ~1 mK. This signal resides at extremely low frequencies (1.3–2.8 MHz, λ ~100–230 m) and is cut off by free–free opacity at z ≳ 1060. Detection would yield constraints on initial conditions at scales far beyond the CMB damping tail (Fialkov et al., 2013).

During the “Dark Ages” (z ~ 30–200), after Compton heating ceases, the IGM cools adiabatically and collisions drive $T_s \to T_K \ll T_{\rm CMB}$ , generating a narrow, weak absorption feature, observable only if an experiment can access ≲50 MHz (Fialkov et al., 2013, Fialkov et al., 2023).

2.2. Cosmic Dawn and the Epoch of Reionization (z ≲ 30)

The emergence of the first luminous objects (stars, galaxies, and possibly black holes) imparts UV photons, activating the Wouthuysen–Field effect (Lyα coupling, typically effective at z ~ 15–25) and driving a deep global absorption trough (expected depth: −100 to −200 mK). As X-ray sources build up, the IGM heats above $T_{\rm CMB}$ , and the signal transitions into emission before being erased by reionization.

Reionization proceeds patchily, driving spatial fluctuations characterized by the 21-cm power spectrum, $\Delta^2_{21}(k,z)$ (Giri et al., 2024). In the late EoR ( $z \lesssim 6$ ), the signal transitions from being dominated by the neutral IGM to tracing HI inside galaxies. Neutral “islands” up to ~40 cMpc persist until the IGM is <10⁻⁴ neutral, imposing a scale-dependent “knee” in $\Delta^2_{21}(k)$ (Giri et al., 2024).

3. Astrophysical and Cosmological Information Content

The 21-cm signal probes a broad set of astrophysical and cosmological phenomena:

Fundamental cosmology & initial conditions: The 21-cm field is a tomographic observable (as opposed to the 2D CMB), probing down to the baryonic Jeans scale at recombination (k ~ 10 Mpc⁻¹), accessing modes inaccessible to the CMB (Fialkov et al., 2013).
Small-scale power and dark matter physics: The signal is sensitive to the matter power spectrum on sub-Mpc scales, constraining warm dark matter free-streaming, isocurvature modes, and primordial non-Gaussianity. For instance, WDM delays and steepens the absorption trough and boosts large-scale 21-cm power; combining the global signal and power spectrum breaks degeneracies with astrophysical parameters (Sitwell et al., 2013).
Nature and properties of early sources: The depth, timing, and spectral shape of the absorption trough can break degeneracies in star-formation efficiency, halo mass function, high-mass X-ray binary heating, and escape fractions. A trough at ν ≲ 90 MHz, a depth shallower than −110 mK, or a strong emission component points to non-standard sources (Mirocha et al., 2016).
Constraints on exotic physics: Energy injection by dark matter decay/annihilation, black hole evaporation, or PMF dissipation modifies IGM temperature, placing strong constraints on new physics from the lack (or depth) of the absorption feature (Natwariya, 2023).

The global signal turning points (timing, depth, and slopes) provide model–independent constraints on the Lyα background, net heating rate, and ionization history, independent of the details of source populations (Mirocha et al., 2013).

4. Measurement Challenges and Experimental Considerations

The 21-cm signal is extremely faint (mK–tens of mK) compared to Galactic and extragalactic foregrounds (T_fg ≳ 10³–10⁵ K at frequencies of interest). Several issues dominate:

Foregrounds: Dominated by synchrotron and free–free emission, with spectral indices that mimic the smooth, broad-band cosmological signal. Accurate modeling to ≲0.1% is required for robust extraction (Liu et al., 2012).
Ionosphere and RFI: Below ~10 MHz, the Earth's ionosphere is opaque; even above this, refraction and absorption by the F- and D-layers introduce spectral structure at percent levels—well above the cosmological signal. Chromatic beam–sky coupling further mixes spatial structure into spectral structure, precluding polynomial subtraction methods (Vedantham et al., 2013, Fialkov et al., 2023).
Cosmic variance: The limited cosmic volume accessible in a thin shell at each frequency introduces an irreducible noise floor (∼0.1 mK for standard models); extreme fluctuation models (e.g., sharp absorption) can yield cosmic variance at the mK level (Muñoz et al., 2020).
Instrument requirements: Angular resolution (θ_b ≲ 10°), wide frequency coverage (ideally 1–200 MHz), stable calibration, and operation from radio-quiet, ionosphere-free sites (lunar farside or Antarctic plateau) are essential for next-generation experiments (Liu et al., 2012, Sun et al., 8 Oct 2025, Fialkov et al., 2023).

5. Analysis Techniques and Statistical Approaches

Global signal recovery: Angular–spectral filtering, full measurement-equation modeling, and the incorporation of external priors (e.g., sky maps, EM beam models, ionospheric data) are critical for minimizing foreground leakage and signal loss (Vedantham et al., 2013, Liu et al., 2012).
Fluctuation statistics: Most analyses employ the spherically averaged 21-cm power spectrum, but the non-Gaussian, patchy structure of the EoR motivates use of higher-order statistics and novel compressed summaries (e.g., Wavelet Scattering Transform, which outperforms the power spectrum in parameter inference) (Greig et al., 2022).
Joint multi-wavelength inference: Constraints from 21-cm global and power spectrum measurements are strengthened when leveraged with UVLFs, CXB/CRB, and upper limits from SARAS, HERA, and SKA-Low, sharply bounding the plausible astrophysical parameter space and providing both upper and lower limits on the absorption trough depth and fluctuation amplitude (Dhandha et al., 19 Aug 2025).
Multi-messenger synergy: Next-generation gravitational-wave observations of high–z black hole mergers can be used to break degeneracies in the star-formation history, leading to significantly improved inference of the astrophysics underlying the 21-cm signal (Tiwari et al., 7 Feb 2026).

6. Experimental Frontiers and Prospects

Detection status: To date, experiments such as EDGES, SARAS, and HERA have reported either tentative detections or increasingly stringent upper limits. Conflicting results regarding claimed absorption features (e.g., the EDGES 78 MHz –500 mK trough) have motivated alternative strategies, such as using the ISW effect in cross-correlation to provide a foreground-immune validation (Ahn et al., 2023).
Global signal vs. power spectrum: Terrestrial experiments are limited by ionospheric cutoff (≳50 MHz), confining access to Cosmic Dawn and EoR but not to the Dark Ages. True detection of the pre-star-formation signal (z > 30, ν < 45 MHz) necessitates lunar or space-based platforms (Fialkov et al., 2023, Fialkov et al., 2013, Yoshiura et al., 1 Feb 2026).
Experiment design: Bayesian evidence analyses demonstrate that band coverage down to <15 MHz is strictly necessary to distinguish cosmological models from foregrounds with high confidence, and that even sparse channelization can suffice if the noise floor is minimized (Yoshiura et al., 1 Feb 2026). Antarctic plateau experiments combine ultra-low RFI, minimal ground reflection, and stable sky patterns, enabling precise calibration and robustness against systematic errors (Sun et al., 8 Oct 2025).

7. Theoretical Modeling and Simulation

Analytic frameworks: Recent progress includes fully analytic, lognormal-based models for the 21-cm global signal and power spectrum, such as Zeus21, which achieves order-10% accuracy versus fully numerical simulations (e.g., 21CMFAST) at much lower computational cost (Muñoz, 2023).
Parameter sensitivity: The global signal is highly sensitive to the star-formation threshold (halo mass floor), the high-redshift X-ray SED and efficiency, and the escape fraction of Lyman–Werner photons. Measurements of the timing and depth of the absorption trough can distinguish between “normal” galaxy-driven models and those that require exotic physics (e.g., Pop III stars or miniquasars) (Mirocha et al., 2016, Muñoz, 2023).

The 21-cm signal constitutes a fundamental observable for next-generation cosmology and astrophysics, offering a unique window on the early universe, the nature of dark matter and dark energy, and the physics of the first structures. Detection and interpretation require a synergy of experimental innovation, rigorous statistical treatment, and detailed physical modeling (Fialkov et al., 2013, Fialkov et al., 2023, Liu et al., 2012, Mirocha et al., 2016, Giri et al., 2024, Dhandha et al., 19 Aug 2025, Yoshiura et al., 1 Feb 2026).