21-cm Cosmology Meets the Neutrino Mass

The cosmic microwave background, anisotropies in the cosmic infrared background, galaxy redshift surveys, weak gravitational lensing, and the Lyman-alpha forest are the workhorses of contemporary cosmological constraints on the neutrino mass. Each probes the matter power spectrum at a specific epoch and on specific scales, and combining them gives the current bound of approximately $\sum m_{\nu }<0.12$ eV from a Planck-plus-baryon-acoustic-oscillation joint analysis. The reach is extraordinary but ultimately limited by the two-dimensional nature of the CMB and the small angular volume that current galaxy surveys cover.

A different probe, just beginning to mature, has the potential to extend the cosmological reach by orders of magnitude. The 21-cm hyperfine line of neutral hydrogen provides a direct three-dimensional map of cosmic structure across redshift ranges that no other technique can access. From the Dark Ages before the first stars formed, through the Cosmic Dawn when those first stars switched on, through the Epoch of Reionisation when their radiation began ionising the intergalactic medium — and on into the post-reionisation universe — neutral hydrogen traces the matter distribution at scales and epochs simply unreachable by anything else.

The neutrino mass enters the 21-cm picture through its effect on structure formation. Massive neutrinos free-stream out of small-scale density perturbations before those perturbations collapse, suppressing the small-scale matter power spectrum by an amount that grows with the neutrino mass. The 21-cm line maps the same matter distribution at the same epochs, so its observed power spectrum directly encodes the neutrino-mass effect. Combining 21-cm observations across redshift with galaxy surveys and CMB data has the potential to push the cosmological neutrino-mass sum bound below 0.04 eV — into the regime where the mass ordering can be determined from cosmology alone.

This post is about how 21-cm cosmology works, what it adds to the neutrino-mass programme, and where the technology stands.

The 21-cm line and what it measures

A neutral hydrogen atom has two hyperfine ground states, differing by the relative spin orientation of the proton and electron. The transition between them emits or absorbs a photon at a rest-frame wavelength of 21.106 cm, corresponding to a frequency of 1.420 GHz. The transition is extraordinarily slow — its spontaneous decay rate gives a $\sim 10$ million year lifetime — but the sheer abundance of hydrogen in the universe makes the line one of the brightest in the radio spectrum.

In a cosmological context, the relevant observable is the brightness temperature of the 21-cm signal as a function of position and observed frequency. The brightness temperature depends on three quantities: the neutral-hydrogen density at the source location, the spin temperature of the hyperfine states, and the cosmic microwave background temperature at the same epoch. Tracking the signal across observed frequency maps directly to redshift through

${\nu }_{\mathrm{obs}}=\frac{1420\mathrm{MHz}}{1+z}$

For sources at redshift $z=10$, the observed frequency is 129 MHz; for $z=30$, the observed frequency is 46 MHz. This is squarely in the long-wavelength radio band, well below the gigahertz range where conventional radio astronomy operates and well below the FM band where terrestrial broadcasts overwhelm the cosmological signal at lower frequencies.

The information encoded in the 21-cm map is the three-dimensional density field of neutral hydrogen across all the relevant cosmological epochs. Because the neutral-hydrogen distribution traces the matter distribution at the relevant times, the 21-cm map is effectively a 3D matter map across redshift.

How neutrinos suppress structure

A massive neutrino with $m_{\nu }\sim 0.05$ eV is non-relativistic by the matter-radiation equality epoch (well after recombination). Its thermal velocity at that epoch is approximately

$v_{\mathrm{th}}\approx \frac{T_{\nu }}{m_{\nu }}\approx 1000km/s\cdot \left(\frac{0.05\mathrm{eV}}{m_{\nu }}\right)$

This is comparable to the velocity dispersion of galaxy clusters today. Density perturbations on scales smaller than the neutrino free-streaming length — the distance a neutrino travels in a Hubble time — cannot trap the neutrinos gravitationally. Instead, the neutrinos free-stream out, and the cold-dark-matter perturbations on those small scales grow more slowly than they would have without the free-streaming neutrinos.

The result is a suppression of the matter power spectrum at scales smaller than the free-streaming length. The suppression amplitude is

$\frac{\Delta P(k)}{P(k)}\approx -8\frac{{\Omega }_{\nu }}{{\Omega }_m}$

at the relevant wavenumbers, where ${\Omega }_{\nu }=\sum m_{\nu }/(94\mathrm{eV})$ is the neutrino density parameter today and ${\Omega }_m$ is the total matter density parameter. For $\sum m_{\nu }=0.06$ eV, the suppression is about 5% — small but measurable with sufficient statistical leverage from a deep 3D survey.

The 21-cm line provides exactly that leverage. Mapping the neutral-hydrogen distribution across redshift gives a three-dimensional matter map at multiple epochs, with the matter power spectrum directly extractable at each redshift. The neutrino-mass suppression appears as a systematic deficit at small scales that grows monotonically with the assumed $\sum m_{\nu }$.

Why the 21-cm window is special

Three properties combine to make the 21-cm probe so attractive for neutrino-mass cosmology.

The first is volume. The CMB is a two-dimensional surface at redshift $\sim 1100$. Galaxy surveys map a three-dimensional region out to redshift $\sim 2$. The 21-cm map covers a three-dimensional volume from redshift $\sim 6$ to $\sim 30$ — a region that is both deeper and dramatically larger than any galaxy survey can reach. The number of independent volume elements (modes) accessible at high redshift exceeds the CMB by orders of magnitude, providing the statistical leverage to detect a small neutrino-mass suppression.

The second is scale. The neutrino-mass-induced suppression is concentrated at small physical scales — wavenumbers $k\sim 0.1$ to $1h/$Mpc — which are easier to measure with high-resolution 3D mapping than with the CMB’s angular resolution at the surface of last scattering. The 21-cm line probes exactly the relevant scales at the relevant redshifts.

The third is early-universe access. The matter power spectrum at $z\sim 10$ is closer to its primordial state than the post-non-linear-evolution power spectrum at $z\sim 0$. This makes the 21-cm signal less affected by the small-scale modelling uncertainties that dominate galaxy-survey systematics at low redshift, and provides a cleaner extraction of the linear-theory predictions where the neutrino mass enters.

The experimental landscape

Several experiments are actively pursuing 21-cm cosmology:

HERA (Hydrogen Epoch of Reionisation Array) operates in the Karoo desert in South Africa. The dedicated 350-element antenna array began observations in 2017 and has been progressively improving the power-spectrum upper limits during the Epoch of Reionisation. HERA’s first detection of the cosmological 21-cm signal is expected in the late 2020s with the full array.

LOFAR and MWA are existing low-frequency radio arrays in the Netherlands and Australia that have observed the 21-cm signal during Epoch of Reionisation, producing upper limits on the signal amplitude.

The Square Kilometre Array (SKA) is the flagship next-generation experiment, being built across South Africa and Australia in two phases. SKA-Mid (mid-frequencies, in South Africa) and SKA-Low (low frequencies, in Australia) will provide unprecedented sensitivity across the full 21-cm redshift range from the Dark Ages through reionisation. SKA-Low’s projected neutrino-mass sensitivity, in combination with CMB-S4 and galaxy surveys, reaches $\sum m_{\nu }<0.04$ eV.

CHIME and the proposed CHORD experiments in Canada have explored post-reionisation 21-cm observations at lower redshift, complementing the high-redshift programmes by mapping the matter distribution at intermediate epochs.

Systematic challenges

The 21-cm signal is faint — typical brightness temperatures of order milli-kelvin against foreground emission three orders of magnitude brighter. Substantial systematic challenges have to be solved:

Foreground subtraction. Galactic synchrotron emission, extragalactic radio sources, and bright point sources in the field of view all produce radio signals far stronger than the cosmological 21-cm signal. Separating the smooth-spectrum foregrounds from the structured signal requires sophisticated subtraction techniques and exquisite calibration.

Radio-frequency interference. The 21-cm cosmological frequency band overlaps with substantial terrestrial radio interference, particularly from FM broadcasts and aviation systems. Antarctic and high-altitude desert sites provide partial protection but not complete.

Reionisation modelling. The brightness temperature of the 21-cm signal during reionisation depends on the spin temperature, which is set by the radiation field of the first stars and quasars. Disentangling the underlying matter distribution from the radiation-field history is non-trivial and requires explicit modelling of the early-universe radiation environment.

Calibration precision. Per-frequency calibration of the radio antennas at the percent level over a wide bandwidth is essential for the spectral-decomposition techniques to work. The required calibration precision pushes radio-astronomy engineering to its limits.

The collective experience of the past decade has been steady progress on each of these challenges, and the projected SKA-era performance assumes their successful resolution.

What a 21-cm detection would deliver

The 21-cm constraints on neutrino mass complement the CMB and galaxy-survey approaches in two important ways.

First, the 21-cm window is sensitive to the same matter perturbations at the same epochs that the CMB extrapolates to, providing a direct measurement at small scales. Combining the two reduces the parameter degeneracies that limit individual analyses — particularly the degeneracy between ${\sigma }_8$ (the matter power spectrum amplitude at $8h^{-1}$ Mpc), the neutrino mass, and the dark energy equation of state.

Second, the 21-cm signal provides constraints on early dark-matter properties that are otherwise inaccessible. Many beyond-Standard-Model neutrino scenarios — partially-thermalised sterile neutrinos, modified neutrino self-interactions, neutrino decay — produce signatures at the 21-cm-window epochs that the CMB sees only indirectly.

For the neutrino-mass sum specifically, the projected SKA-era bound of $\sum m_{\nu }<0.04$ eV is below the minimum allowed by the inverted-mass-ordering scenario (~$0.10$ eV). A detection of a 21-cm signal consistent with $\sum m_{\nu }<0.06$ eV would essentially force the normal ordering, providing an independent confirmation of the result expected from JUNO, DUNE, and ORCA. A detection above 0.10 eV would be inconsistent with the normal-ordering prediction and would either confirm the inverted ordering or point to new cosmological physics.

Summary

The 21-cm hyperfine line of neutral hydrogen provides a three-dimensional probe of cosmic structure across the redshift range $z=6$ to $30$ — accessing volumes orders of magnitude larger than galaxy surveys can map and reaching epochs far earlier than the CMB can resolve. Massive neutrinos suppress the matter power spectrum at small scales through free-streaming, and the 21-cm map of neutral hydrogen at the relevant epochs directly encodes the suppression. Current experiments (HERA, LOFAR, MWA) are producing first power-spectrum upper limits in the Epoch of Reionisation. The Square Kilometre Array, in operation from the late 2020s, will reach projected sensitivity to the neutrino-mass sum below $\sum m_{\nu }\sim 0.04$ eV — below the inverted-mass-ordering minimum. Combined with CMB-S4 and DESI, the 21-cm programme will deliver a cosmological determination of the neutrino mass sum at the level required to constrain the mass ordering from cosmology alone, providing one of the independent inputs that — combined with oscillation experiments and beta-decay endpoint measurements — will pin down the absolute neutrino mass across multiple complementary probes.