Cold freeze out of superheavy dark matter and Hubble tension

TL;DR

This paper introduces the "X miracle" framework where superheavy dark matter particles form compact states, leading to a cold freeze-out that may resolve the Hubble tension and produce observable gravitational waves and ultralight axions.

Contribution

It proposes a novel superheavy dark matter model based on gravitational collapse and quantum effects, linking dark matter to neutrino mass, baryogenesis, and observable signatures.

Findings

A viable dark matter candidate with mass ~10^{12} GeV.

Potential to generate ΔN_eff ≈ 0.4, easing Hubble tension.

Predictions include high-frequency gravitational waves and ultralight axions.

Abstract

We propose a unified dark matter framework, the "X miracle", in which dark matter consists of superheavy, nonthermal X particles whose relic abundance is set by annihilation or decay inside the earliest self-gravitating bound objects, rather than by conventional weak-scale freeze-out of semi-relativistic WIMPs. X particles are produced nonthermally with an initial overabundance $\rho_{ini}\gg\rho_{\infty}$, become nonrelativistic extremely early, and redshift to ultra-cold velocities. This permits collapse into compact bound states characterized by a quantum-gravitational radius $r_X=4\hbar^2/Gm_X^3=10^{-13}$m, much larger than the Compton wavelength. The framework favors a mass $m_X=10^{12}$GeV and an enhanced effective cross section $10^{-21}$m$^3$/s. Overlapping wavefunctions in these compact states drive efficient annihilation or decay, producing a "cold" freeze-out that converts most $\rho_{ini}$ into radiation and leaves a small relic density $\rho_{\infty}$. Solving Boltzmann equations shows that a level of depletion of one surviving particle per $10^9$ can generate $\Delta N_{eff}\approx$0.4, potentially easing Hubble tension. For $m_X=10^{12}$GeV we obtain a dark coupling $\alpha_X=0.09$, compatible with UHECR limits. Early collapse at $t\sim 10^{-6}$s can release binding energy in high-frequency (~100 kHz) gravitational waves or in ultralight GUT-scale axions with mass ~$10^{-9}$eV. Superheavy sterile neutrinos offer a natural particle realization, linking dark matter to neutrino mass generation and baryogenesis; gravitational production of X then points to high-scale inflation with efficient reheating. The X-miracle scenario demonstrates that dark matter need not be weak-scale: its abundance and observable signatures can instead be governed by small-scale gravitational dynamics, with correlated predictions for UHECRs, axions, gravitational waves, and small-scale structures.