Superheavy dark matter and stepped dark radiation for Hubble Tension

Manuscript and CSV data behind the figure and table of Xu (2026), Superheavy dark matter and stepped dark radiation for Hubble Tension, Research Square preprint, doi:10.21203/rs.3.rs-8570078/v3. The earlier data record of this work is zenodo.org/records/23001771. Contents: the manuscript (P05_revised.pdf) and the folder csv/ with the plotted data of Fig. 2 (free-streaming mass against particle mass) and the component densities of Table 1. Companion dataset: the cold freeze-out paper, Xu (2025), Eur. Phys. J. C 85, 1451, doi:10.1140/epjc/s10052-025-15180-z, data record doi:10.5281/zenodo.23934750. Major findings: The free-streaming mass equals the particle mass at m_Xc = 1.6×10-15 kg = 0.9×1012 GeV. A two-body gravitational bound state of 1012 GeV particles has a size of 1.2×10-13 m, an internal speed of 5×10-7 m/s and forms at tX = 5×10-7 s (T ≈ 1 GeV). The gravity-induced bulk velocity of dark matter is frozen during radiation domination at 8–9 km/s. Cold freeze-out leaves a relic fraction γ ≈ 10-9 (8×10-10 for 1012 GeV); ΔNeff = 0.4 needs a dark-radiation share fDR ≈ 0.2 of the converted energy. In the stepped dark-radiation embedding, the measured drag RΓ = 0.07 gives a DM–DR Yukawa coupling λX ≈ 8×10-5; a Planck-suppressed portal gives yK ≈ 7×10-15 and a no-scale supergravity scalar mass of about 0.5 eV. Gravitational production with γ ≈ 10-8 needs HI ≈ 1012 GeV, TRH ≈ 1015 GeV and a tensor-to-scalar ratio r ≈ 2×10-5.