Superheavy dark matter and stepped dark radiation for Hubble Tension

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 that alleviates 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 critical particle mass $10^{12}$ GeV. As the Universe cools, X becomes ultra-cold and, when the thermal speed falls below the gravity‑induced velocity on the order of km/s, collapses into the smallest compact bound states at $10^{-6}$ s, in which quantum pressure balances gravity leading to a new scale $r_X\simeq10^{-13}$m, producing 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 naturally 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 $10^{-4}$, consistent with observations, while a Planck‑suppressed spurion portal induces a tiny coupling $10^{-14}$ that governs conversion inside compact states. 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 yields clear targets for CMB and structure surveys, as well as future probes of dark sector self‑interactions.