Abstract
<title>Abstract</title> <p>The persistent Hubble tension motivates new early-universe physics that reduces the sound horizon while remaining consistent with CMB and structure data. We present a framework \REV{that alleviates the Hubble tension}{that provides a candidate mechanism to alleviate the Hubble tension} with superheavy nonthermal dark matter (DM) X, in which gravity, rather than a thermal freeze-out, sets the relic abundance. A free streaming analysis identifies a preferred mass scale $m_X\simeq10^{12}$ GeV as the unique mass at which the free-streaming mass equals the individual particle mass, delineating the regime where Newtonian quantum gravity becomes relevant. As the Universe cools, overproduced $X$ becomes ultra-cold; when the thermal speed falls below the gravity‑induced linear peculiar velocity (km/s), the initial DM density becomes comparable to the radiation density at $t_X\simeq10^{-6}$ s. This enables gravitational collapse to a quantum-gravitational bound state, in which quantum pressure balances gravity leading to a new quantum-gravity scale $r_X\simeq10^{-13}$ m, providing an enhanced effective cross section of $\langle\sigma v\rangle\simeq10^{-21}$ m$^3$s$^{-1}$ and a “cold” freeze‑out that converts most of the initial overabundance $n_i$ into dark radiation (DR). Solving the Boltzmann equation gives a relic density $n_{\infty} = \gamma n_i$ with $\gamma\sim10^{-9}$, producing $\Delta N_{eff}\simeq0.4$ that raises the CMB‑inferred $H_0$. We realize this cosmology in a minimal dark sector built on the stepped WZDR dark radiation framework: a renormalizable Yukawa generates DM–DR drag with a coupling $\lambda_X=10^{-4}$, consistent with observations, while a Planck‑suppressed spurion portal induces a tiny coupling $y_{\REV{k}{K}}=10^{-14}$ that governs \REV{conversion inside compact states}{portal-mediated bound-state conversion to dark radiation}. A high-scale SUSY breaking $\sqrt{F}\simeq10^{12}$GeV fixes particle mass $m_X$, and embedding in a no-scale supergravity cancels the tree‑level gravity‑mediated soft mass so that the scalar acquires subleading contributions $F^2/M_{Pl}^3$, naturally at the eV‑scale. This framework links macroscopic cold freeze‑out to microscopic couplings, and \REV{yields clear targets}{suggests targets} for CMB and structure surveys, as well as future probes of dark sector interactions.</p>