Superheavy dark matter from structure formation and X miracle

Abstract: We propose a new theory of dark matter based on structure formation at the free-streaming scale (the smallest structure scale) and an "X miracle" beyond the standard WIMP paradigm. Both approaches point to superheavy fermionic dark matter with a mass of $10^{12}$ GeV. Unlike low-mass WIMPs that are weakly interacting, semi-relativistic at freeze-out, and unaffected by gravity, the X miracle applies to heavy dark matter and incorporates gravitational effects, introducing a new fundamental scale $r_X=4\hbar^2/Gm_X^3=10^{-13}m\gg \hbar/m_Xc$, breaking the unitarity bound and allowing for a cross section as large as $10^{-21}$m$^3$/s. At the critical mass of $10^{12}$GeV, the free streaming mass matches particle mass, enabling the earliest and smallest gravitationally bound structures to form at $10^{-6}$s after the Big Bang. The collapse of these structures can release binding energy as high-frequency (100 kHz) gravitational waves (GWs) or as ultralight GUT-scale underabundant axions. Superheavy sterile neutrinos could be natural dark matter candidates, potentially addressing neutrino mass and baryogenesis. Solutions to the nonequilibrium Boltzmann equation suggest a significant early dark matter annihilation or decay leading to a relic DM abundance, with one in a billion dark matter particles surviving. This scenario offers explanations for ultra-high-energy cosmic rays (UHECRs) and Hubble tension. The predicted cross sections of $10^{-21}$m$^3$/s, energy production rate density of $10^{45}$erg Mpc$^{-3}$ Yr$^{-1}$, and particle lifetime of $10^{23}$years are well within UHECR observational constraints. If gravitationally produced, these superheavy X particles also suggest high-scale inflation and efficient reheating. The X miracle highlights that dark matter need not be weak-scale but could emerge from gravity, with observational signals in UHECRs, axion, GWs, and structure formation.