📝 SummarXiv

Abstract

We present the "X miracle", a framework in which dark matter consists of superheavy, nonthermal X particles whose relic abundance arises not from the weak-scale, semi-relativistic ("hot") freeze-out of WIMPs, but from annihilation or decay within the smallest and earliest gravitationally bound objects. Unlike thermal WIMPs, which decouple at V$\sim$0.3c with relic density set by weak-scale interactions, X particles are produced nonthermally with an initial overabundance $\rho_{ini}\gg\rho_{\infty}$, become nonrelativistic very early, and redshift to ultra-cold velocities, allowing them to collapse into compact bound structures characterized by a quantum-gravitational scale, $r_X=4\hbar^2/Gm_X^3=10^{-13}m\gg\hbar/m_Xc$. The framework predicts $m_X=10^{12}$GeV with an enhanced cross section of $10^{-21}$m$^3$/s. Overlap of particle wavefunctions in these compact structures drives a "cold" freeze-out that converts most $\rho_{ini}$ into radiation while leaving a relic density $\rho_{\infty}$. The exact solution to the Boltzmann equation reveals an extreme depletion, with only one particle in a billion surviving, resulting in an extra radiation $\Delta N_{eff}\approx$0.4, which potentially alleviates the Hubble tension. The framework predicts an energy production rate density $10^{45}$erg Mpc$^{-3}$Yr$^{-1}$ and particle lifetime $10^{16}$years (or coupling $\alpha_X=0.09$), consistent with UHECR limits. Early collapse at $10^{-6}$s may release high-frequency (100kHz) gravitational waves or ultralight GUT-scale axions. Superheavy sterile neutrino is a natural candidate, linking dark matter to neutrino mass and baryogenesis. If gravitationally produced, the model favors high-scale inflation and efficient reheating. The X miracle demonstrates that gravitational interaction can control freeze-out and evolution, producing multi-messenger signatures in UHECRs, axions, and gravitational waves.