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We study the consequences of new long-range forces between neutrinos on cosmic scales. If these forces are a few orders of magnitude stronger than gravity, they can induce perturbation instability in the nonrelativistic cosmic neutrino background in the late time universe. As a result, the cosmic neutrino background may form nonlinear bound states instead of free-streaming. The implications of the formation of nonlinear neutrino bound states include enhancing matter perturbations and triggering star formation. Based on existing measurements of the matter power spectrum and reionization history, we place new constraints on long-range forces between neutrinos with ranges lying in $1\mathrm{kpc}\lesssim m_{\varphi }^{-1}\lesssim 10\mathrm{Mpc}$. Published by the American Physical Society2025 

Abstract We discuss Dirac neutrinos whose right-handed component ν R has new interac­tions that may lead to a measurable contribution to the effective number of relativistic neutrino species N eff . We aim at a model-independent and comprehensive study on a variety of possibilities. Processes for ν R -genesis from decay or scattering of thermal species, with spin-0, spin-1/2, or spin-1 initial or final states are all covered. We calculate numerically and analytically the contribution of ν R to N eff primarily in the freeze-in regime, since the freeze-out regime has been studied before. While our approximate analytical results apply only to freeze-in, our numerical calculations work for freeze-out as well, including the transition between the two regimes. Using current and future constraints on N eff , we obtain limits and sensitivities of CMB experiments on masses and couplings of the new interactions. As a by-product, we obtain the contribution of Higgs-neutrino interactions, Δ N eff SM ≃ 7.5 × 10 -12 , assuming the neutrino mass is 0.1 eV and generated by the standard Higgs mechanism.