Superheavy dark matter and stepped dark radiation for Hubble Tension

Abstract

The persistent Hubble tension motivates early-universe physics that reduces the sound horizon while remaining consistent with CMB and large-scale structure data. We present a framework in which the relic abundance of superheavy nonthermal dark matter (DM) $X$ is set by gravity rather than thermal freeze-out. Several independent considerations point to a commonmass scale $m_X\simeq10^{12}\,$GeV: a free-streaming analysis identifies it as the unique mass at which the free-streaming mass equals the particle mass, marking the onset of a Newtonian quantum-gravity regime; the gravity-induced bulk peculiar velocity in the radiation era is then of order km\,s$^{-1}$; and UV/IR mixing together with the DM--DR drag independentlyselect the same scale. These results apply equally to standard dark-matter cosmologies, independently of any overproduction. In the overproduction scenario, the initially overabundant $X$ becomes ultra-cold as the Universe expands; the DM density becomes comparable to the radiation density at $t_X\simeq10^{-6}\,$s. This triggers gravitational collapse to a bound state in which quantum pressure balances gravity, setting a quantum-gravitational scale $r_X\simeq10^{-13}\,$m. Within these states the overlapping wavefunctions convert most of the overabundance into dark radiation (DR) at very low relative velocity---a ``cold'' freeze-out---leaving a relic $n_\infty=\gamma\,n_i$ with $\gamma\sim10^{-9}$, hence $\Delta N_{\rm eff}\simeq0.4$ and a raised CMB-inferred $H_0$. We realize this in a minimal dark sector built on the stepped WZDR dark-radiation framework: a renormalizable Yukawa generates the DM--DR drag with coupling $\lambda_X\sim10^{-5}$, while a Planck-suppressed spurion portal induces a tiny coupling $y_K\sim10^{-14}$. High-scale SUSY breaking $\sqrt{F}\simeq m_X\simeq10^{12}\,$GeV fixes the DM mass, and a no-scale supergravity embedding cancels the tree-level gravity-mediated soft mass, so the scalar acquires a subleading $F^2/M_{\rm Pl}^3$ contribution naturally at the eV scale. The framework links a macroscopic cold freeze-out to microscopic couplings and suggests targets for CMB and structure surveys and future probes of dark-sector interactions.