The Cosmic Neutrino Background is within Reach of Future Neutrino Telescopes

Abstract

The cosmic neutrino background (C$ν$B) can be boosted to high energies due to scatterings with energetic cosmic rays (CRs) across cosmological scales. Previous calculations focused on neutral current incoherent and coherent elastic scatterings of cosmic-ray protons off relic neutrinos. However, charged current interactions and deep inelastic scatterings are also expected to occur, which enhances the boosted relic neutrino fluxes on Earth. Here, we compute the \textit{total} diffuse boosted cosmic neutrino background (DBC$ν$B) arising from CRs at all redshifts in the Universe, accounting for neutral current and charged current elastic and deep inelastic scatterings. We find that IceCube already places an upper limit on the cosmic neutrino background overdensity in cosmological scales of ~$\mathcal{O}(100-1000)$ at $E_ν=10^{10}$ GeV, for a lightest neutrino mass of $m_ν \gtrsim 0.1$ eV. We further show that IceCube-Gen2 could test $\mathcal{O}(1-10)$ C$ν$B overdensities, and the combination of $10$ future neutrino telescopes with similar sensitivity would allow us to test the $Λ$CDM expected C$ν$B density for a lightest neutrino mass compatible with the KATRIN bound.

Figures (3)

• Figure 2: Left panel: The C$\nu$B flux boosted by CR protons via different scattering channels, summed over all three flavors. The light blue bands indicate the contributions from CC quasi-elastic interactions, via either $\beta$ decay or $\mu^{\pm}$ decay. The blue colored band corresponds to the NC elastic scattering channel, already computed in Ref. herrera2025diffuse. The dark blue band corresponds to our NC DIS contribution. The thickness of the bands reflects the uncertainty in the CR source evolution. In solid blue lines, we further show the boosted C$\nu$B fluxes from the Milky Way and TXS 05056+056 Ciscar-Monsalvatje:2024tvm. All predictions shown assume a neutrino mass of $m_\nu=0.1$ eV. For comparison, we present the total flux of atmospheric neutrinos and diffuse extragalactic neutrinos measured by terrestrial experiments Super-Kamiokande:2015qekIceCube:2016umiIceCube:2020acn, along with the current upper limits on ultra-high-energy neutrinos from IceCube (green, IceCubeCollaborationSS:2025jbi), Auger (dark red, PierreAuger:2015ihf), and ANITA I-IV (red, ANITA:2018ANITA:2019wyx). Sensitivity projections for IceCube-Gen2 radio (10 yr) (dooted green, IceCube-Gen2:2021rkf) and the expected range of cosmogenic-neutrino fluxes (grey band, Fang:2017zjfGRAND:2018iaj) are also displayed. Right panel: Same as left panel, but zoomed in the NC DIS part. In blue shading is the ultra-high-energy "neutrino fog" induced by the deep-inelastically boosted C$\nu$B (labeled DBC$\nu$B, DIS, QSO). The upper end of the blue colored region corresponds to CRs following the QSO evolution function.
• Figure 3: Left panel: Current and projected upper limits on the C$\nu$B overdensity ($\eta$) versus lightest neutrino mass, for different CR models and normal (inverted) neutrino mass hierarchies in solid (dashed). The best limit is obtained from a combination of the elastic and deep-inelastic scatterings. For neutrino masses to the left (right) of the dotted vertical gray line, elastic (deep-inelastic) scattering drives the most stringent limit. Limits set by NC elastic and NC DIS processes respectively can be found in the the Appendix \ref{['sec:ES_and_DIS_limits']}. The dashed orange line denotes the maximum $\eta$ allowed by Pauli principle on cosmological scales Bondarenko:2023ukx (see Appendix \ref{['sec:neutrino_overdensity']}). The upper bound on the lightest neutrino mass from KATRIN is shown as a shaded red region KATRIN:2024cdt. Right panel: Projected upper limits on the C$\nu$B from a combination of 10 future experiments with comparable sensitivity at ultra-high energies to IceCube-Gen2, both for a background-free scenario (dubbed "BKG free"), and for a background-dominated scenario (dubbed "BKG dominated). For comparison, we also show the IceCube-Gen2 only projected sensitivity.
• Figure 4: Left panel: Current and projected limits set by ES processes. Different colors represent different CR source evolutions. Solid lines are current limits, dashed lines are projected limits. Opaque lines indicate normal neutrino mass ordering, and translucent ones indicate inverted ordering; Right panel: Same as left panel, but with DIS processes considered.