Paper detail

Cold freeze out of superheavy dark matter and Hubble tension

We propose a unified dark matter framework, the "X miracle", in which dark matter consists of superheavy, nonthermal X particles whose relic abundance is set by annihilation or decay inside the earliest self-gravitating bound objects, rather than by conventional weak-scale freeze-out of semi-relativistic WIMPs. X particles are produced nonthermally with an initial overabundance $ρ_{ini}\ggρ_{\infty}$, become nonrelativistic extremely early, and redshift to ultra-cold velocities. This permits collapse into compact bound states characterized by a quantum-gravitational radius $r_X=4\hbar^2/Gm_X^3=10^{-13}$m, much larger than the Compton wavelength. The framework favors a mass $m_X=10^{12}$GeV and an enhanced effective cross section $10^{-21}$m$^3$/s. Overlapping wavefunctions in these compact states drive efficient annihilation or decay, producing a "cold" freeze-out that converts most $ρ_{ini}$ into radiation and leaves a small relic density $ρ_{\infty}$. Solving Boltzmann equations shows that a level of depletion of one surviving particle per $10^9$ can generate $ΔN_{eff}\approx$0.4, potentially easing Hubble tension. For $m_X=10^{12}$GeV we obtain a dark coupling $α_X=0.09$, compatible with UHECR limits. Early collapse at $t\sim 10^{-6}$s can release binding energy in high-frequency (~100 kHz) gravitational waves or in ultralight GUT-scale axions with mass ~$10^{-9}$eV. Superheavy sterile neutrinos offer a natural particle realization, linking dark matter to neutrino mass generation and baryogenesis; gravitational production of X then points to high-scale inflation with efficient reheating. The X-miracle scenario demonstrates that dark matter need not be weak-scale: its abundance and observable signatures can instead be governed by small-scale gravitational dynamics, with correlated predictions for UHECRs, axions, gravitational waves, and small-scale structures.