### Fermions and gravitational gyrotropy *[Cross-Listing]*

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In conventional general relativity without torsion, high-frequency gravitational waves couple to the chiral number density of spin one-half quanta: the polarization of the waves is rotated by $2\pi N_5 {\ell _{\rm Pl}^2}$, where $N_5$ is the chiral column density and $\ell _{\rm Pl}$ is the Planck length. This means that if a primordial distribution of gravitational waves with E-E or B-B correlations passed through a chiral density of fermions in the very early Universe, an E-B correlation in the waves, and one in the cosmic microwave background, would be generated. Less obviously but more primitively, the condition Albrecht called `cosmic coherence’ would be violated, changing the restrictions on the class of admissible cosmological gravitational waves.