Einstein–Cartan Torsion, Fermionic Freeze-In, and Ultralight Dark Matter

Einstein–Cartan (EC) gravity induces a contact interaction between axial fermion currents that can produce gauge-singlet fermions in the early Universe. For ultraviolet-dominated 2→2 production we derive the spectrum f(q) ∝ q e⁻ᵠ, with mean momentum 4T at production (4.11T for Fermi–Dirac initial states) and present temperature T_χ = 7.80 × 10⁻⁵ eV. A linear Boltzmann calculation maps the Lyman-α limits on thermal relics, 5.3 and 3.5 keV, onto m_χ ≥ 24.5 keV and m_χ ≥ 14.1 keV; phase-space bounds are weaker, 0.8–3.4 keV. In the minimal theory a keV-scale candidate needs a reheating temperature above the CMB bound on the inflation scale, so such masses require an enhanced torsion coupling. EC-produced fermions cannot form an ultralight composite boson: non-Goldstone bound states weigh about 2m_χ, and a Goldstone boson of their condensate would be heavier than 10⁶ GeV. For an ultralight scalar coupled to the torsion-induced currents, the decisive constraint on a shift-breaking coupling is zero-temperature radiative stability, |c| ≲ 2 × 10⁻³¹; thermal tadpoles are far weaker inside the validity range of the contact interaction, because the leading thermal average of A·A is m_f² T⁴ / 36 per Dirac fermion and vanishes for massless fermions. Shift-symmetric couplings are observable through an axion-wind energy of order 10⁻³² eV at f_φ = 10¹⁷ GeV. The EC portal is thus a viable warm-dark-matter mechanism above about 25 keV, and not a fuzzy-dark-matter mechanism.