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 ρ∞ set by weak-scale interactions, X particles are produced nonthermally with an initial overabundance ρᵢₙᵢ ρ∞. 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 10¹²GeV 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 ρᵢₙᵢ into radiation while leaving a relic density ρ∞. Solutions to the Boltzmann equation indicate that an extreme depletion, with only one particle in a billion surviving, yields an additional radiation contribution Δ Neff≈0.4, which could help alleviate the Hubble tension. For particles of 10¹²GeV, the scenario predicts an energy production rate density of 10⁴⁵erg Mpc⁻³Yr⁻¹ and particle lifetime 10¹⁶years (or coupling αX=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.