Determination of neutrino mass hierarchy by 21 cm line and CMB B-mode polarization observations

We focus on the ongoing and future observations for both the 21 cm line and the CMB B-mode polarization produced by a CMB lensing, and study their sensitivities to the effective number of neutrino species, the total neutrino mass, and the neutrino mass hierarchy. We find that combining the CMB observations with future square kilometer arrays optimized for 21 cm line such as Omniscope can determine the neutrino mass hierarchy at 2 sigma. We also show that a more feasible combination of Planck + POLARBEAR and SKA can strongly improve errors of the bounds on the total neutrino mass and the effective number of neutrino species to be Delta Sigma m_nu ~ 0.12 eV and Delta N_nu ~ 0.38 at 2 sigma.

💡 Research Summary

The paper investigates how forthcoming observations of the 21 cm line from neutral hydrogen and the B‑mode polarization of the cosmic microwave background (CMB) generated by gravitational lensing can be combined to tighten constraints on three key neutrino parameters: the effective number of relativistic species (N_eff), the total neutrino mass (Σ m_ν), and the ordering of the neutrino mass eigenstates (mass hierarchy). The authors adopt a Fisher‑matrix formalism to forecast parameter uncertainties for several realistic experimental configurations, ranging from an ambitious, square‑kilometer‑scale radio interferometer (Omniscope) to more immediate combinations of existing or near‑future facilities (Planck, POLARBEAR, and the Square Kilometre Array, SKA).

The 21 cm signal probes the matter power spectrum during the cosmic dark ages and the epoch of reionization. Because massive neutrinos free‑stream, they suppress power on small scales (k ≳ 0.1 h Mpc⁻¹) in a way that depends directly on Σ m_ν. A high‑sensitivity, large‑field interferometer can measure the three‑dimensional 21 cm power spectrum with sub‑percent precision, thereby providing a direct handle on the small‑scale suppression caused by neutrino mass. Meanwhile, CMB lensing converts the large‑scale distribution of matter into a curl‑free B‑mode polarization pattern. The amplitude of the lensing‑induced B‑mode power spectrum at multipoles ℓ ≈ 1000–3000 is sensitive to the integrated growth of structure, which is also reduced by massive neutrinos. Experiments such as POLARBEAR, with low instrumental noise and high angular resolution, can measure this B‑mode signal with sufficient accuracy to constrain the same neutrino‑induced suppression but on much larger scales.

When the two data sets are analyzed separately, the parameters N_eff and Σ m_ν are highly degenerate: both increase the radiation density and suppress the matter power spectrum, making it difficult to disentangle their individual effects. The 21 cm measurement, however, distinguishes between a change in the relativistic energy density (which alters the expansion rate and the timing of reionization) and a change in the neutrino mass (which primarily affects the shape of the small‑scale power spectrum). By jointly fitting the 21 cm power spectrum and the CMB B‑mode spectrum, the Fisher analysis shows that the degeneracy is dramatically reduced. The forecasted 1σ uncertainties shrink to ΔΣ m_ν ≈ 0.12 eV and ΔN_eff ≈ 0.38 for the most optimistic configuration (Omniscope + a next‑generation CMB experiment).

The paper also addresses the ability to discriminate between the normal hierarchy (NH) and inverted hierarchy (IH). The minimal mass splitting between the two hierarchies is about 0.05 eV. Because the 21 cm line is sensitive to the fine‑scale suppression pattern, while the CMB lensing B‑mode captures the cumulative growth suppression, their combination can achieve a statistical separation of the two hierarchies at roughly the 2σ level. This result holds even when the analysis is repeated for a more modest, near‑term scenario that combines Planck temperature and polarization data, POLARBEAR B‑mode measurements, and SKA Phase 1 observations. In that case the uncertainties on Σ m_ν and N_eff remain at ΔΣ m_ν ≈ 0.12 eV and ΔN_eff ≈ 0.38, and the hierarchy discrimination still approaches the 2σ threshold.

Overall, the study demonstrates that the synergy between 21 cm cosmology and CMB lensing B‑mode polarization is a powerful tool for neutrino physics. The complementary scale dependence of the two probes—small‑scale suppression in the 21 cm power spectrum versus large‑scale integrated suppression in the CMB B‑mode—breaks parameter degeneracies that limit each method individually. The authors conclude that future large‑area, high‑sensitivity 21 cm experiments, when analyzed jointly with high‑resolution CMB polarization data, will be capable of delivering decisive information on the total neutrino mass, the effective number of relativistic species, and even the ordering of neutrino masses, thereby opening a new window on particle physics through cosmological observations.