Cosmogenic Neutrinos: The Guaranteed Flux Above the GZK Cutoff

High-energy neutrino astronomy has a well-known frontier at the PeV scale — IceCube’s astrophysical diffuse flux, the TXS 0506+056 blazar, the steady source NGC 1068. But there is a second, higher frontier that has been predicted with unusual confidence for nearly sixty years and yet remains entirely unobserved: the cosmogenic neutrino flux at energies around an exa-electronvolt ($10^{18}$ eV), three orders of magnitude above IceCube’s highest-energy events.

What makes cosmogenic neutrinos special is not that they are exotic but that they are nearly inevitable. They are a direct consequence of two well-established facts: ultra-high-energy cosmic rays exist, and the cosmic microwave background fills all of space. Put those two together and the production of neutrinos follows from particle physics that has been measured in accelerators. The cosmogenic flux is, in this sense, the most robustly predicted neutrino source in all of astrophysics — and detecting it is one of the defining goals of the next generation of neutrino observatories.

This post is about the GZK mechanism that produces these neutrinos, why the flux is so confidently predicted yet so hard to observe, and the radio-detection techniques being deployed to find it.

The GZK cutoff

In 1966, shortly after the discovery of the cosmic microwave background, Kenneth Greisen and — independently — Georgiy Zatsepin and Vadim Kuzmin pointed out a consequence that the new radiation field imposed on cosmic rays. A proton travelling through space at sufficiently high energy will see the cold microwave photons blueshifted in its own rest frame. If the proton’s energy is high enough, those blueshifted photons carry enough energy to excite the proton to the ${\Delta }^{+}(1232)$ resonance:

$p+{\gamma }_{\text{CMB}}\to {\Delta }^{+}\to n+{\pi }^{+}$

or, through the competing channel,

$p+{\gamma }_{\text{CMB}}\to {\Delta }^{+}\to p+{\pi }^0$

The threshold for this reaction sits at a proton energy of roughly $5\times 10^{19}$ eV when colliding with a typical CMB photon. Above that threshold, the cross-section is large because it is resonant, so the proton loses a substantial fraction of its energy in each interaction. The mean free path becomes short — only a few megaparsecs — and the proton’s energy degrades after each collision until it drops below threshold.

The practical consequence is the GZK horizon: protons above $\sim 5\times 10^{19}$ eV cannot reach us from farther than roughly 50 to 100 megaparsecs. The cosmic-ray spectrum should therefore show a sharp suppression above this energy. That suppression was confirmed by the HiRes experiment and the Pierre Auger Observatory in the late 2000s, although whether the observed feature is purely the GZK effect or partly reflects the maximum energy of the sources themselves is still debated.

From the cutoff to neutrinos

The pion produced in the GZK reaction is the seed of the neutrino flux. A charged pion is unstable and decays:

${\pi }^{+}\to {\mu }^{+}+{\nu }_{\mu }$

and the muon in turn decays:

${\mu }^{+}\to e^{+}+{\nu }_e+{\bar{\nu }}_{\mu }$

So a single charged-pion decay chain yields three neutrinos — one ${\nu }_{\mu }$, one ${\bar{\nu }}_{\mu }$ and one ${\nu }_e$ — plus a positron. The neutral pion from the competing channel decays to two gamma rays rather than neutrinos, feeding instead an electromagnetic cascade that contributes to the diffuse gamma-ray background.

Each neutrino carries away roughly 5% of the original proton’s energy, so a proton near $10^{20}$ eV produces neutrinos in the neighborhood of a few times $10^{18}$ eV. This is why the cosmogenic flux peaks around the exa-electronvolt scale — far above anything IceCube has detected, which tops out near a few PeV ($10^{15}$ eV).

Why the flux is so confidently predicted

Most astrophysical neutrino fluxes depend on uncertain source models — how efficiently a blazar jet accelerates protons, how dense the target radiation field is, how the source population evolves over cosmic time. The cosmogenic flux sidesteps much of this because its target is not a particular source but the cosmic microwave background itself, whose density and spectrum are known to exquisite precision from cosmology.

The remaining uncertainties are real but bounded. The biggest is the composition of ultra-high-energy cosmic rays. If they are mostly protons, the GZK mechanism operates efficiently and the neutrino flux is relatively high. If they are heavier nuclei such as iron — as some Pierre Auger composition measurements suggest at the highest energies — then the dominant energy-loss process is photodisintegration rather than pion production, and the cosmogenic neutrino flux is substantially lower. The second major uncertainty is the cosmological evolution of the sources: more distant, earlier-universe sources contribute neutrinos that have been produced against a denser, hotter CMB, which boosts the flux.

These uncertainties span perhaps two orders of magnitude in the predicted flux — significant, but the existence of some cosmogenic flux is not in doubt. This is qualitatively different from speculative dark-matter or exotic-physics signals. The cosmogenic flux must be there; nature has no choice in the matter once cosmic rays and the CMB both exist.

The detection challenge

The problem is the smallness of the flux. At $10^{18}$ eV the predicted event rate corresponds to something like one neutrino interaction per cubic kilometer of water-equivalent per decade or worse. IceCube, with its one cubic kilometer of instrumented ice optimized for the PeV scale, simply does not have enough volume to catch these rarer, higher-energy events at a useful rate. Its searches have produced only upper limits.

Reaching the cosmogenic flux requires monitoring volumes of hundreds to thousands of cubic kilometers. Optical Cherenkov detection — the technique IceCube uses, with thousands of photomultipliers reading out Cherenkov light in clear ice — does not scale economically to that size, because light is absorbed and scattered over distances of tens to a hundred meters and the sensors must be spaced accordingly.

The way out is radio detection, which exploits the Askaryan effect. When an ultra-high-energy neutrino interacts in a dense dielectric medium such as cold ice, the resulting particle shower develops a net negative charge excess (electrons are swept in from the surrounding material while positrons annihilate). This moving charge excess radiates coherent radio waves in the gigahertz range. Crucially, radio waves propagate through cold ice with an attenuation length of a kilometer or more — ten to a hundred times farther than optical light. A sparse array of radio antennas can therefore instrument an enormous volume with relatively few sensors.

A complementary approach watches for the radio or optical signals from neutrino-induced air showers, particularly Earth-skimming tau neutrinos that interact in the ground, produce a tau lepton that emerges from a mountainside or the Earth’s limb, and decay in the atmosphere to start an upward-going shower.

The experimental landscape

Several experiments pursue this frontier. ANITA, a balloon-borne radio antenna array flown over Antarctica, searched for radio pulses from neutrino interactions in the ice sheet across multiple flights and reported a pair of anomalous upward-going events that, while probably not neutrinos, generated considerable discussion. ARA (Askaryan Radio Array) and ARIANNA are ground-based radio arrays deployed in Antarctic ice as pathfinders for the technique. The planned radio component of IceCube-Gen2 would instrument roughly 500 cubic kilometers with radio stations specifically to reach the cosmogenic flux. GRAND (Giant Radio Array for Neutrino Detection) proposes a vast array of radio antennas across mountainous terrain to catch Earth-skimming tau neutrinos over an effective area approaching $200,000$ square kilometers.

The radio detectors built and tested so far have confirmed that the technique works — they detect cosmic-ray air showers via their radio emission, which validates the calibration — but none has yet reached the sensitivity needed to guarantee a cosmogenic detection within a reasonable observing time, especially if the cosmic-ray composition is heavy. The next decade, with IceCube-Gen2 radio and GRAND coming online, is when a detection becomes plausible.

Why it matters

Detecting the cosmogenic flux would do more than confirm a sixty-year-old prediction. The flux carries information that is otherwise inaccessible. Its magnitude directly constrains the proton fraction of ultra-high-energy cosmic rays — a question that optical and fluorescence cosmic-ray detectors have struggled to settle. Its energy spectrum encodes the cosmological evolution of the sources, because neutrinos from the early universe were produced against a denser CMB and arrive at characteristic energies. And because neutrinos travel undeflected by magnetic fields and unabsorbed across cosmological distances, the cosmogenic flux is the only messenger that can probe the universe’s particle accelerators at the very highest energies and the very largest distances simultaneously.

A non-detection is also informative. If sensitive experiments run for years and see nothing, that increasingly favors a heavy cosmic-ray composition and disfavors the proton-dominated scenarios, sharpening one of the central open questions in cosmic-ray physics. Either way, the exa-electronvolt frontier is where the next qualitative step in neutrino astronomy is likely to come from.

Summary

Cosmogenic neutrinos arise inevitably when ultra-high-energy cosmic rays collide with cosmic microwave background photons, the same process that produces the GZK suppression of the cosmic-ray spectrum above $5\times 10^{19}$ eV. The flux peaks near $10^{18}$ eV and is the most robustly predicted neutrino source in astrophysics, depending mainly on the proton fraction of cosmic rays and the cosmological evolution of their sources. Detection demands instrumenting hundreds to thousands of cubic kilometers, which is the goal of radio-detection experiments exploiting the Askaryan effect — ARA, ARIANNA, the IceCube-Gen2 radio array, and GRAND. As of 2025 only upper limits exist, but a detection in the coming decade would settle long-standing questions about the origin and composition of the highest-energy particles in the universe.