Cold freeze out of superheavy nonthermal dark matter

Abstract We present a unified framework, the "X miracle", in which dark matter consists of superheavy, nonthermal X particles whose relic abundance is determined not by the conventional weak-scale, semi-relativistic ("hot") freeze-out of WIMPs, but by annihilation or decay occurring within the smallest and earliest gravitationally bound objects. Unlike thermal WIMPs, which decouple at velocities of order 0. 3c with relic abundance _ set by weak-scale interactions, X particles are produced nonthermally with an initial overabundance ₈₍₈ _. They become nonrelativistic extremely early, redshift to ultra-cold velocities, allowing collapse into compact bound structures characterized by a novel quantum-gravitational scale, rX=4²/GmX³=10^-13m /mXc, much larger than the Compton wavelength. The framework predicts a particle mass of 10^12GeV and an enhanced cross section of 10^-21m³/s. Overlapping particle wavefunctions in these compact structures drive annihilation or decay into additional radiation, leading to a "cold" freeze-out that converts most of ₈₍₈ into radiation while leaving a relic density _. Solutions to the Boltzmann equation indicate that an extreme depletion, with only one particle in a billion surviving, yields an additional radiation contribution N₄₅₅0. 4, which could help alleviate the Hubble tension. For particles of 10^12GeV, the scenario predicts an energy production rate density of 10^45erg Mpc^-3Yr^-1 and particle lifetime 10^16years (or coupling X=0. 09), consistent with current UHECR bounds. Early collapse at 10^-6s may release binding energy as high-frequency (100kHz) gravitational waves or ultralight GUT-scale axions. Superheavy sterile neutrinos provide a natural particle physics realization, linking dark matter to neutrino mass and baryogenesis. If gravitational production dominates, this framework favors high-scale inflation and efficient reheating. The "X miracle" thus demonstrates that dark matter need not be weak-scale: gravitational dynamics can control freeze-out and evolution, producing multi-messenger observational signatures in UHECRs, axions, gravitational waves, and small-scale structures.