Cold freeze out of superheavy dark matter and Hubble tension

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 0.3 c with relic abundance $$\rho _{\infty }$$ ρ ∞ set by weak-scale interactions, X particles are produced nonthermally with an initial overabundance $$\rho _{ini}\gg \rho _{\infty }$$ ρ ini ≫ ρ ∞ . They become nonrelativistic extremely early, redshift to ultra-cold velocities, allowing collapse into compact bound structures characterized by a novel quantum-gravitational scale, $$r_X=4\hbar ^2/Gm_X^3=10^{-13}m\gg \hbar /m_Xc$$ r X = 4 ħ 2 / G m X 3 = 10 - 13 m ≫ ħ / m X c , much larger than the Compton wavelength. The framework predicts a particle mass of $$10^{12}$$ 10 12 GeV and an enhanced cross section of $$10^{-21}$$ 10 - 21 m $$^3$$ 3 /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 $$\rho _{ini}$$ ρ ini into radiation while leaving a relic density $$\rho _{\infty }$$ ρ ∞ . Solutions to the Boltzmann equation indicate that an extreme ("big") depletion, with only one particle in a billion surviving, yields an additional radiation contribution $$\Delta N_{eff}\approx $$ Δ N eff ≈ 0.4, which could help alleviate the Hubble tension. For particles of $$10^{12}$$ 10 12 GeV, the scenario predicts a dark coupling constant $$\alpha _X=0.09$$ α X = 0.09