Joint 21-cm and CMB forecasts for constraining self-interacting massive neutrinos

Self-interacting neutrinos provide an intriguing extension to the Standard Model, motivated by both particle physics and cosmology. Recent cosmological analyses suggest a bimodal posterior for the coupling strength $G_{\rm eff}$, favoring either strong or moderate interactions. These interactions modify the scale-dependence of the growth of cosmic structures, leaving distinct imprints on the matter power spectrum at small scales, $k\,>\,0.1\,{\rm Mpc}^{-1}$. For the first time, we explore how the 21-cm power spectrum from the cosmic dawn and the dark ages can constrain the properties of self-interacting, massive neutrinos. The effects of small-scale suppression and enhancement in the matter power spectrum caused by self-interacting neutrinos propagate to the halo mass function, shaping the abundance of small- and intermediate-mass halos. It is precisely these halos that host the galaxies responsible for driving the evolution of the 21-cm signal during the cosmic dawn. We find that HERA at its design sensitivity can improve upon existing constraints on $G_{\rm eff}$ and be sensitive to small values of the coupling, beyond the reach of current and future CMB experiments. Crucially, we find that the combination of HERA and CMB-S4 can break parameter degeneracies, significantly improving the sensitivity to $G_{\rm eff}$ over either experiment alone. Finally, we investigate the prospects of probing neutrino properties with futuristic Lunar interferometers, accessing the astrophysics-free 21-cm power spectrum during the dark ages. The capability of probing small scales of these instruments will allow us to reach a percent-level constraint on the neutrino self-coupling.