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

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 to dilute the dark matter abundance revives the natural inflation. Since the dark matter must be a spin zero scalar, we study carefully 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 $\gamma$-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, $\alpha_s\gtrsim\mathcal{O}(0.001)$, 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 coordinates may provide insight into not only the origin of the cosmic rays but also inflation.