Spacetime torsion fixes the mass and spin of gravitationally produced dark matter

Abstract

The gravitational production of dark matter from stochastic gravitational waves requires the produced fermion to acquire a mass by unspecified late-time physics. We show that this mass is supplied by spacetime torsion alone -- no Higgs sector and no free mass parameter. In the Quadratic Spinor Lagrangian formulation of general relativity, extended to Einstein--Cartan, a cosmological spinor condensate generates a vectorial trace torsion $K\propto \dot{\chi }/\chi$; an explicit Clifford reduction confers on the produced spin-1/2 fermion a pure Dirac mass $M_{\mathrm{eff}}=(1/\sqrt{6})|\dot{\chi }/\chi |$, with no pseudoscalar or cross terms, locked to the Hubble rate at production, $M_{\mathrm{eff}}\simeq (c_{\chi }/\sqrt{6})H_{\ast }$. The relic abundance is then a one-parameter prediction, $\Omega h^2\propto H_{\ast }^{5/2}$, and the spin is fixed: the same framework admits no propagating spin-3/2 mode, so the composite spin-1/2 Dirac fermion is its unique dark-matter candidate.

3 pages, 1 figure