21 cm Intensity Mapping in Cosmology

Updated 5 February 2026

21 cm intensity mapping is a technique that integrates the 21 cm emission from neutral hydrogen to produce three-dimensional maps of the Universe's large-scale structure.
It employs various instruments and survey designs to measure power spectra and bispectra, extracting signatures like baryon acoustic oscillations and redshift-space distortions.
Robust data analysis, including advanced foreground subtraction and simulation-driven methods, enables precision measurements of cosmic parameters and the HI–halo mass relation.

21 cm intensity mapping (IM) is a technique that measures spatial fluctuations in the integrated 21 cm hyperfine emission from neutral hydrogen (HI) across cosmological volumes, without attempting to resolve individual galaxies or sources. Unlike traditional galaxy redshift surveys, which catalog the positions and velocities of discrete objects, IM surveys the summed emission within each resolution element (“voxel”) as a function of angle and frequency, producing three-dimensional maps of the large-scale structure (LSS) of the Universe extending from $z \sim 0$ to $z > 6$ . This approach leverages the fact that, post-reionization, most HI is bound within dark matter halos, so the 21 cm intensity field tracks the cosmic web and encodes a wealth of cosmological information, including baryon acoustic oscillations (BAO), redshift-space distortions (RSD), and the HI halo mass relation (HIHM).

1. Theoretical Framework

The fundamental observable is the 21 cm brightness-temperature fluctuation field, which at position $\mathbf{x}$ and redshift $z$ is

$\delta T_b(\mathbf{x},z) = \bar T(z)\,\frac{\rho_{\rm HI}(\mathbf{x},z)}{\bar\rho_{\rm H}} - \bar T(z) \,,$

where

$\bar T(z) = 4\,\mathrm{mK}\,(1+z)^2\,\frac{\Omega_b h^2 / 0.02}{h/0.7}\,\frac{H_0}{H(z)}$

is the mean differential brightness temperature, $\rho_{\rm HI}(\mathbf{x},z)$ the spatial HI density, and $\bar\rho_{\rm H}$ the mean hydrogen density [$2508.19126$].

The Fourier modes $\delta T_b(\mathbf{k})$ define the key statistical measures:

Power spectrum: $\langle \delta T_b(\mathbf{k})\,\delta T_b(-\mathbf{k}')\rangle = (2\pi)^3\,\delta_D(\mathbf{k}-\mathbf{k}')\,P_T(k)$
Bispectrum: $\langle \delta T_b(\mathbf{k}_1)\,\delta T_b(\mathbf{k}_2)\,\delta T_b(\mathbf{k}_3)\rangle = (2\pi)^3\,\delta_D(\mathbf{k}_1+\mathbf{k}_2+\mathbf{k}_3)\,B_T(k_1,k_2,k_3)$

The HI density field is modeled, at large scales, by a local deterministic bias expansion,

$\delta_{\rm HI}(\mathbf{x}) = b_1\,\delta(\mathbf{x}) + \frac{b_2}{2}\,\delta^2(\mathbf{x}) + \ldots,$

where $b_1$ and $b_2$ are the linear and quadratic HI bias parameters and $\delta$ the matter overdensity. This expansion forms the basis for predicting the 21 cm PS and BS from the matter PS, with prefactors encoding HI abundance and bias, and for reconstructing the underlying HI–halo relation from large-scale measurements [$2508.19126$].

2. Instrumentation, Survey Design, and Sensitivity

21 cm intensity mapping can be implemented with single-dish telescopes, cylinder reflectors, or interferometric arrays, each with characteristic strengths:

Instrument	Type	Frequency/Redshift Range	Survey Area	Thermal Noise (T_sys)	Example
BINGO	Single-dish	960–1260 MHz (z~0.13-0.48)	2000 deg²	50 K	(Battye et al., 2016)
FAST	Single-dish	400–1420 MHz (z~0–2.5)	20,000 deg²	20 K	(Smoot et al., 2014, Wu et al., 2022)
SKA1-MID	Dishes	0.35–0.8 (z), up to z~3	20,000 deg²	$T_{\rm sys}(\nu)$	(Wu et al., 2022)
HIRAX	Interferometer	400–800 MHz (z~0.77–2.55)	15,000 deg²	50 K	(Wu et al., 2022)
DSA-2000	Interferometer	700–2000 MHz (z~0–1)	1700 deg²	25 K	(Byrne et al., 2023)
CHIME	Cylindrical	400–800 MHz (z~0.8–2.5)	$\sim$ 1000 deg²	50 K	(Collaboration et al., 24 Nov 2025)

Key survey parameters include angular and spectral resolution (typically $1'$–$10'$ and $<1$ MHz), sky area, field-of-view, and total integration time. Sensitivity forecasts require computing the thermal noise, beam window function, and the accessible $k$ -range, accounting for sample (cosmic) variance and shot noise [$1610.06826$, $2212.07681$, $2311.00896$].

3. Foreground Subtraction, Systematics, and Data Analysis

Foregrounds exceeding the cosmological 21 cm signal by 4–5 orders of magnitude (predominantly Galactic synchrotron) necessitate aggressive subtraction and/or avoidance strategies:

Blind subtraction (e.g., PCA, SVD) projects out the largest eigenmodes in frequency-space, but inevitably incurs some cosmological signal loss and residual contamination due to foreground–signal subspace overlap [$2208.14675$].
Semi-blind methods, such as Singular Vector Projection (SVP), exploit external knowledge of foreground singular vectors in frequency and/or spatial space, achieving order-of-magnitude improvements in signal recovery. The optimal SVP estimator is

$\hat{N}_D = D - U_f\,\mathrm{diag}(U_f^T D V_f)\,V_f^T$

where $D$ is the data cube, and $U_f$ , $V_f$ the known foreground singular vectors [$2208.14675$].

Foreground avoidance isolates clean regions of $(k_\perp,k_\parallel)$ -space, excluding the so-called wedge, at the cost of losing information on large radial scales [$2602.03313$].

Systematics such as polarization leakage, spectral mismodeling, RFI, and calibration stability are addressed via bespoke data-processing pipelines, e.g., radiometer/statistical flagging, achromatic beamforming, and pre-stacking filtering [$2511.19620$]. Validation includes null and cross-correlation tests with optical catalogues to ensure the robustness of the recovered cosmological signal.

4. Cosmological Applications and Information Content

21 cm intensity mapping delivers three-dimensional maps of the cosmic HI distribution, enabling a suite of cosmological and astrophysical measurements:

Large-Scale Structure and BAO: The 21 cm PS detects the BAO wiggles (e.g., as shown with BINGO, DSA-2000, FAST) yielding constraints on the distance scale $D_A(z)$ and expansion history $H(z)$ with fractional errors $\sim1$ –$2$\% at $z\sim0.8$ –2.5 [$1610.06826$, $1407.3583$, $2311.00896$].
Redshift-Space Distortions (RSD): The anisotropic PS quantifies the growth rate $f(z)$ and combination $f\sigma_8(z)$ , constraining structure formation and testing gravity [$2212.07681$, $1212.0728$].
Dark Energy and Modified Gravity: Joint analyses (e.g., FAST+SKA1-MID+HIRAX) attain $\sigma(w)\sim0.019$ , $\sigma(w_0)\sim0.085$ , and $\sigma(w_a)\sim0.32$ , matching or surpassing CMB+BAO+SNe combinations, and enable principal-component tests of time- and scale-dependent gravity [$2212.07681$, $1212.0728$].
HI–Halo Mass Relation: The shape and amplitude of the 21 cm PS and BS at large scales constrain the HIHM parameters—the normalization $\alpha$ , slope $\beta$ , and cutoff $v_{c0}$ —with $10$–$50$\% precision depending on external priors on $\Omega_{\rm HI}$ [$2508.19126$].
Epoch of Reionization (EoR) and Cross-Correlations: At $z>6$ , cross-power spectra between 21 cm and line-intensity maps ([C II], CO) tomographically constrain the ionization fraction $x_e(z)$ and minimum mass of ionizing sources to $9$– $40\sigma$ per redshift bin [$2512.13943$].

5. Recent Detections and Practical Realizations

21 cm IM has transitioned from cross-correlation detections with optical surveys to high-significance auto-correlation measurements:

CHIME: Achieved the first $>10\sigma$ auto-power detection at $z\sim1$ across $0.4<k<1.5\,h\,{\rm Mpc}^{-1}$ using rigorous RFI excision, time-domain foreground filtering, and achromatic beamforming. The extracted $\mathcal{A}=1.26^{+1.09}_{-0.65}$ (amplitude) agrees with external cross-survey results, demonstrating that 21 cm auto-PS can robustly constrain $\Omega_{\rm HI}b_{\rm HI}(z)$ without external tracers [$2511.19620$].
GBT and Parkes: Provided both upper bounds (auto-PS) and lower bounds (cross-correlation with galaxies) at $z\sim0.8$ , constraining $\Omega_{\rm HI}b_{\rm HI}=(0.62^{+0.23}_{-0.15})\times10^{-3}$ [$1304.3712$].
BINGO, FAST, DSA-2000, SKA1-MID: Simulations and design studies confirm that wide-area, deep integrations can deliver percent-level cosmological constraints, especially with optimized foreground control, calibration, and, for arrays, the inclusion of densely packed short baselines to enable low- $k$ and BAO mode sensitivity [$1610.06826$, $1407.3583$, $2311.00896$].

6. Forward Modeling, Simulations, and Future Prospects

Rapid advances in simulation methodology underpin the interpretation and pipeline validation for 21 cm IM:

Cosmological Remapping: Large-volume halo catalogs can be transformed to new cosmologies via spatial, mass, and displacement rescaling (“Angulo–White remapping”), then populated with HI using empirically calibrated HOD models. This approach delivers 21 cm mocks accurate to $\leq 10\%$ in PS for $k\lesssim0.1\,h\,{\rm Mpc}^{-1}$ , enabling cosmology-marginalized pipeline testing at $<1\%$ computational cost relative to new $N$ -body runs [$2506.14588$].
Deep Learning Mode Recovery: BAO information lost to wedge excision and mode removal can be partially reconstructed directly from short-wavelength data by exploiting non-linear mode-coupling learned from simulations. Network-based restoration recovers BAO phase with high fidelity, imparting robustness to observational analyses even in the presence of realistic noise [$2602.03313$].
Foreground Immunity via One-Point Statistics: Novel one-point cross-statistics (e.g., the Conditional Voxel Intensity Distribution Ratio, CVR) enable direct measurement of the HI mass function, including the faint, optically undetected population, without reference to the power spectrum or detailed foreground modeling [$1907.04369$].

Lensing, patchy reionization, and nonlinear astrophysics pose additional modeling challenges. For surveys probing to high multipole $\ell_{\rm max}>700$ , lensing of the 21 cm PS requires modeling second- and third-order perturbative corrections, including new post-Born terms absent in CMB studies [$1807.01351$].