Equation of State of the Torsion Spin Fluid at Late Times

This paper derives the late-time equation of state of the spin-torsion correction treated as a cosmic fluid. In Einstein-Cartan gravity the spin contribution enters the effective density with a negative sign and, for a conserved fermion number, scales as the sixth power of the inverse scale factor. A component with that scaling has pressure equal to its (negative) energy density in magnitude, corresponding to a stiff index for the magnitude, yet its present density is fixed by the bounce normalisation rather than chosen freely. Normalising the term so that it cancels the ordinary density at the neutron-carrier density limit gives a present magnitude far below every observed cosmic component. The mixed dark-sector equation of state therefore remains indistinguishable from a cosmological constant at all redshifts probed by supernovae and baryon acoustic oscillations. Headline values are: rho tor today kg m3 = 7.431e-112, rho DE obs kg m3 = 5.836e-27, ratio today = 1.273e-85, w at z1 = -1.000e+00, ratio at z10 = 3.681e-82. This study is simulated and computed from stated assumptions; it is not a measurement.