Cosmological Origin of the KM3-230213A event and associated Gravitational Waves

TL;DR

We address the KM3-230213A ultra-high-energy neutrino event by proposing that primordial black hole evaporation in the early Universe produces a super-heavy sterile neutrino $N_1$ that decays after neutrino decoupling to yield $\mathcal{O}(100)$~PeV neutrinos, redshifted to today. The model embeds a type-I seesaw with three sterile states; two ($N_2,N_3$) generate light neutrino masses while a feebly coupled $N_1$ accounts for the observed flux, and the same framework predicts two high-frequency gravitational-wave signatures from PBH evaporation and graviton bremsstrahlung in $N_1$ decay. A cosmological lepton asymmetry is generated mainly by $N_2$ and $N_3$ decays (not by $N_1$), enabling successful leptogenesis even with the extra PBH-produced component, and BBN/vacuum-stability constraints are checked (e.g., $M_{N_2,N_3}$ within $10^{14}$–$10^{15}$ GeV). The proposal yields testable, correlated multi-messenger signals: an isotropic UHE neutrino flux with a defined spectral peak and ultra-high-frequency GW backgrounds, offering a novel link between high-energy neutrino astronomy and early-Universe GW cosmology.

Abstract

We propose a novel cosmological scenario to explain the exceptional KM3-230213A neutrino event reported at an energy scale of $\mathcal{O}(100)$~PeV by the KM3NeT collaboration, along with its associated gravitational wave (GW) signatures. In our framework, ultra high energy neutrinos originate from the decay of a super-heavy sterile neutrino produced via the Hawking evaporation of primordial black holes (PBHs) in the early Universe. Employing an ultraviolet complete type-I seesaw model, we demonstrate that while two sterile neutrinos are responsible for light neutrino masses as required by oscillation data, one sterile neutrino can have an exceedingly feeble coupling, allowing its lifetime to be tuned so that its decay yields a neutrino flux consistent with the observed event. Furthermore, our scenario predicts two distinct GW signatures: one arising from gravitons emitted during PBH evaporation and another from the Bremsstrahlung process during the decay of the sterile neutrino. These complementary signals provide a multi-messenger probe of the underlying physics. Our results thus offer a compelling explanation for the KM3-230213A event and open new avenues for investigating the interplay between high-energy neutrino astronomy and gravitational wave cosmology.

Figures (9)

• Figure 1: Evolution of the comoving energy densities for radiation, PBH, and sterile neutrinos (left) and the sterile neutrino number density (right) as functions of the scale factor for two different sterile neutrino masses, $m_{N_1}=10^{-2} M_p$ and $0.1 M_p$. Here, we take the initial PBH mass as $M_{\rm in} = 1$ g.
• Figure 2: Predicted single flavor neutrino flux from decays of superheavy sterile neutrinos ($m_{N_1}=0.1 M_p$), produced via PBH evaporation, shown for PBH mass $M_{\rm in}=1 \ \rm{g}$ and $\beta=5 \times 10^{-22}$. Different colored curves represent different Yukawa couplings governing the sterile neutrino decay rate.
• Figure 3: [Left]: The allowed parameter space in the $\beta$ versus $m_{N_1}/M_p$ plane for two different initial primordial black hole masses: $M_{\rm{in}} = 1~\rm{g}$ and $M_{\rm{in}} = 10^2~\rm{g}$ where the color gradient represents the corresponding Yukawa coupling $|Y_{\alpha 1}|$ values. [Right]: The parameter space in the $|Y_{\alpha 1}|$ versus $m_{N_1}/M_p$ plane for $M_{\rm{in}} = 1~\rm{g}$, with the color gradient indicating the $\beta$ values and the red solid lines represent contours of constant sterile neutrino lifetime $\tau_{N_1}$.
• Figure 4: Gravitational wave spectrum from direct evaporation of PBHs for different initial masses, $M_{\rm in} = 1 \ \rm{g}$, $10^4 \ \rm{g}$, and $10^8 \ \rm{g}$. The solid lines correspond to the full numerical evaluation including greybody factors, whereas the dashed lines show the analytical approximation as in Eq. (\ref{['eq:omGW_PBHevap']}). Here, we have fixed $\beta = 10^{-21}$.
• Figure 5: Feynman diagrams representing the decay of sterile neutrino $N_1$ into neutrino ($\nu$) and SM Higgs $h$ along with a graviton ($h_{\mu\nu}$) bremsstrahlung.