Superheavy dark matter from the natural inflation in light of the highest-energy astroparticle events

TL;DR

This work investigates a scenario in which the inflaton of natural inflation also serves as superheavy DM, stabilized by a dark-charge symmetry and diluted by a temporary dark-energy phase to match the observed DM abundance. The authors analyze the inflationary dynamics, deriving slow-roll parameters and connecting them to CMB observables, while identifying viable regions in parameter space that yield $m_\phi$ in the $10^9$–$10^{13}$ GeV range and predict a detectable tensor-to-scalar ratio. They study the DM decay channels into SM and dark-sector final states, compute multi-messenger fluxes, and show that certain channels can marginally explain the AMATERASU event or the KM3NeT KM3-230213A data within gamma-ray bounds. To alleviate gamma-ray constraints, they propose a dark-sector decay path (including a mirror SM) that predominantly yields neutrons, predicting distinctive high-energy neutron signatures and potential collider-accessible light colored states, thereby linking UHECR observations to inflationary physics. The work thus offers a cohesive framework where high-energy cosmic-ray data inform inflationary parameters (e.g., a lower bound on the tensor-to-scalar ratio and running of the spectral index) and illuminate possible signatures of new dark-sector or mirror-SM physics in future experiments.

Abstract

Superheavy dark matter has been attractive as a candidate of particle dark matter. We propose a ``natural" particle model, in which the dark matter serves as the inflaton in natural inflation, while decaying to high-energy particles at energies of $10^{9}-10^{13} \, \text{GeV}$ from the prediction of the inflation. A scalar field responsible for diluting the dark matter abundance revives the natural inflation either with or without the recent data from the Atacama Cosmology Telescope (ACT) and baryon acoustic oscillation results from Dark Energy Spectroscopic Instrument. Since the dark matter must be a spin-zero scalar, we carefully study the galactic dark matter 3-body decay into fermions and two body decays into a gluon pair, and point out relevant multi-messenger bounds that constrain these decay modes. Interestingly, the predicted energy scale may coincide with the AMATERASU event and/or the KM3NeT neutrino event, KM3-230213A. We also point out particle models with dark baryon to further alleviate $γ$-ray bounds. This scenario yields several testable predictions for the UHECR observations, including the highest-energy neutrons that are unaffected by magnetic fields, the tensor-to-scalar ratio, the running of spectral indices, $α_s\gtrsim\mathcal{O}(0.001)$, and the existence of light new colored particles that could be accessible at future collider experiments. Further measurements of high-energy cosmic rays, including their components and detailed directions, may provide insight into not only the origin of the cosmic rays but also inflation.

Figures (5)

• Figure 1: The contour of the running $\alpha_s$ in the viable parameter space. In the gray shaded region in the top, this scenario does not achieve a field value $\theta_*$ consistent with the observed spectral index. This figure also shows constraints from the tensor-to-scalar ratio (green shaded region in the right bottom) and the running of the spectral index (red shaded region in the bottom) required for successful inflation. The green dashed line represents the contour for $r=0.001$, up to which could be probed by future measurements.
• Figure 2: The left panel shows the contours of the axion mass while the right panel shows the countours of reheating temperature to explain the observed DM abundance. Above the $T_R=1.8 {\rm \, MeV}$ line (bold black line), one needs to consider other scenarios, e.g., a second inflation driven by $\Psi$. We fix $N_{*}$ to be consistent with the thermal histry of the early universe.
• Figure 3: [Left top] The integrated photon fluxes for the decay channel, $\phi \rightarrow H q \bar{q}$, with $m_\phi = 10^9, \, 10^{11}, \, 10^{13}, \,10^{15} \, {\rm \, GeV}$, that just sastify the photon limits. The limits from KASCADE, KASCADE-Grande KASCADEGrande:2017vwf, and Auger Savina:2021cvaPierreAuger:2022uwdPierreAuger:2022aty are also shown. [Right top] The upper limits of the DM decay rates. The green star indicates the grean dashed lines ($m_\phi = 10^{13} {\rm \, GeV}$) in other figures relevant to the AMATERASU event. [Left bottom] The corresponding averaged fluxes of the CR $p+\bar{p}+n+\bar{n}$. The black data points from Auger are taken from PierreAuger:2019phh. The colored ones are from the TA experiment Sagawa:2022glkTelescopeArray:2018xyi. The red point corresponds to the AMATERASU particle TelescopeArray:2023sbd. Following Poisson statistics, we express the uncertainty up to $3\sigma$. [Right bottom] The fluxes of $\frac{1}{3}\sum \nu+\bar{\nu}$. The blue and orange points represent the best-fit data point by KM3NeT and the IceCube-KM3Net joint data point, respectively KM3NeT:2025npi. The other data are shown as NST (purple points) Abbasi:2021qfz, HESE (green points) IceCube:2020wum, and Glashow resonance event(light blue points) IceCube:2021rpz. Also, the dashed lines represent upper limits from IceCube-EHE (90% CL IceCube:2025ezc), Auger (90% CL PierreAuger:2023pjg), and ANTARES (90% CL ANTARES:2024ihw). The error bars for the KM3NeT data indicate the $1,2,3 \sigma$ uncertainties.
• Figure 4: Same as Fig. \ref{['fig:Hqq']} but assuming the channel, $\phi \rightarrow \bar{H} \bar{l} l$. In the right-top panel, the red star corresponds to the KM3-230213A event in addition to those for the AMATERASU event (green star).
• Figure 5: Same as Fig. \ref{['fig:Hqq']} but assuming the channel, $\phi \rightarrow gg$.